{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/v1598-line","json":"https://aaronspradlin.grok.me/page.json?slug=v1598-line","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"v1598-line","title":"v15.98 through v16.55, then A12","dek":"Research branches only. None merged to main. v16.55 is a bounded guard on the integration branch. The 10 Oct overlapping-guard tip records scoped C3 closeouts. Spare capacity is not reachable reserve, and that is not a general no-go. Not numbered v16. Not a source. Not Einstein.","updated":"2026-10-10","status":"result","claim":"restricted","tags":["v16.55","A12","research-branch","not-status"],"related":["v1578-line","research-ladder","live-gates","falsification"],"packages":[{"id":"uqcf-gem-v13","name":"ResearchHistory/UQCF-GEM (v13–v14)","path":"ResearchHistory/UQCF-GEM","status":"restricted"}],"notes":[],"claims":[{"id":"atlas:v15-98","status":"restricted","text":"v15.98, research/v15.98-composed-four-body-response, commit 3a3655a, not merged. COMPOSITION_ORDER_GEOMETRY_CONFIRMED and COMMUTING_COMPOSITION_ACTIVATION_CONFIRMED. Four-body exposure does not require noncommutation. Order contrast is a separate measurement. Not gravity."},{"id":"atlas:v15-99-invalid","status":"restricted","text":"v15.99, research/v15.99-intermediate-eb-retention, not merged. Both preregistered verdicts are INVALID. Rank covariance failed. Predicates that evaluate true do not override validity. Not a certified physical result."},{"id":"atlas:v16-13f","status":"restricted","text":"v16.13F, not merged. RETAINED_FOUNDATION_PARTIALLY_CLOSED_WITH_TYPED_BOUNDARY and INTRINSIC_OBSTRUCTION_COMPOSITION_UNDERDETERMINED. The missing object is obstruction transport. Not a metric, not a quantum carrier, not Einstein. scientific_breakthrough: false."},{"id":"atlas:v16-32","status":"restricted","text":"v16.32, not merged. NONINJECTIVE. The value-level closure earned through v16.31 does not reconstruct the underlying indexed retained cover. Smallest witness: three vertices, two views."},{"id":"atlas:v16-35","status":"restricted","text":"v16.35, research/v16.35-fiber-barrier-closure, not merged. Eighteen pairs of consistency-equivalent retained states have a positive exact barrier: every legal one-incidence path must leave the endpoint quotient. The barrier coordinates are not energies, times, or geometric distances."},{"id":"atlas:v16-36","status":"restricted","text":"v16.36 RESULTS.md, frozen at merge ce4f0c0 on research/v16.34-fiber-component-invariant, 30 Sep 2026, not on main. Gates A and B CLOSED. Gate C is BOUNDED NO-COLLISION. Gate D is UNRESOLVED. LOCAL_UNIT is not claimed. Gate E is not a universal ultrametric theorem. The earlier verifier recomputed each supplied pair and did not independently prove that all 18 required pairs were present. PR #80 (d887068) added the P1–P8 proof ledger and did not close that gap. PR #81 enumerates the canonical universe, requires exact record equality, and rejects omissions, duplicates, and same-count substitutions. Post-merge audit 36731692842, workflow head 8941af1, froze ce4f0c0, reconstructed 18 records, and passed the inherited stack. No scientific conclusion changed. Signature C uses attainable tau on the minimax-feasible subgraph, so it still depends on the certified barrier and is not an independent predictive law. Next obligation, not a result: prove that factorization in general, or find a counterexample."},{"id":"atlas:v16-37","status":"restricted","text":"v16.37, research/v16.37-certified-closure, not on main. Every rooted unordered tree with 1–5 vertices and k in {1,2,3}: 51 graphs, 6325 states, 77 endpoint pairs, zero nonunit pairs. BOUNDED_UNIT_ONLY. Universal unit law UNRESOLVED. Audit receipt e5c3e33."},{"id":"atlas:v16-38","status":"restricted","text":"v16.38, merge e4de671, not on main. Every rooted unordered tree with 1–6 vertices and k in {1,2,3}: 111 graphs, 52907 states, 1497 endpoint pairs, zero nonunit pairs. BOUNDED_UNIT_ONLY. Universal unit law UNRESOLVED. Audit receipt ed87aef."},{"id":"atlas:v16-39","status":"restricted","text":"v16.39, commit c934fee, not on main. Sufficient saturation condition for unit barriers, independently reviewed as sound. Not preregistered. No new numerical execution. Not a characterization. Not numbered-stage certified."},{"id":"atlas:v16-40","status":"restricted","text":"v16.40, research/v16.40-coordinate-obstruction, not on main. One fixed tree. MOVING_LOCATION_WITNESS_VALIDATED: a unit path whose deviation coordinate changes. A single fixed coordinate is not enough for that pair. indecomposable_fixed_coordinate UNRESOLVED. Not a smallest-witness theorem. Not physical energy. Universal unit barrier UNRESOLVED."},{"id":"atlas:v16-41","status":"restricted","text":"v16.41, research/v16.41-unit-barrier-dichotomy, not on main. PARTITION_THEOREM_VALIDATED_BOUNDED_REMAINDER_UNIT for partition profiles on finite rooted no-unary trees with k equal to the leaf count and q equal to outdegree. Intrinsic indecomposability NOT_CLAIMED. Finite remainder had zero nonunit pairs. Universal unit barrier UNRESOLVED."},{"id":"atlas:v16-42","status":"restricted","text":"v16.42, research/v16.42-overlapping-core-repair, not on main. FAMILY_THEOREM_VALIDATED for the reviewed T(d,m) family only. Intrinsic indecomposability is not claimed. Universal unit barrier UNRESOLVED."},{"id":"atlas:v16-43","status":"restricted","text":"v16.43, research/v16.43-star-fiber-classification, not on main. STAR_CLASSIFICATION_VALIDATED: exact hitting-number fibers of a rooted star with m and k at least 2 are one component, except the packed case m=k=q. The packed case has m! isolated components of one profile, every pair at barrier 1. Height 1 is not one component and not one move. Nested interactions UNRESOLVED."},{"id":"atlas:v16-44","status":"restricted","text":"v16.44, research/v16.44-two-branch-unit-barrier, not on main. TWO_BRANCH_THEOREM_VALIDATED for every admitted no-unary rooted tree with exactly two internal vertices and k at least 2. Barriers are 1 between distinct exact components. Universal unit barrier UNRESOLVED."},{"id":"atlas:v16-45","status":"restricted","text":"v16.45, research/v16.45-binary-fork-unit-barrier, not on main. Family theorem, not one graph: every admitted binary root with two star children, arbitrary leaf degrees and palette size in that domain. Total L1 at most 1. Barrier 0 inside an exact component. B1, Binf, and Bs are each 1 between distinct exact components. Chains, extra root children, and arbitrary trees stay out. Not a physical evolution."},{"id":"atlas:v16-46","status":"restricted","text":"v16.46, research/v16.46-nested-chain-repair, not on main. NON_SATURATED_CHAIN_LEMMA_VALIDATED when the outer target is strictly below its degree. The saturated outer root was left UNRESOLVED at this gate. Universal unit barrier UNRESOLVED."},{"id":"atlas:v16-47","status":"restricted","text":"v16.47, research/v16.47-saturated-chain-repair, not on main. THREE_INTERNAL_CHAIN_THEOREM_VALIDATED: every three-internal-vertex chain of degrees at least 2 and k at least 2 admits total L1 excursion at most 1, including the saturated outer root. Not arbitrary branching. Universal unit barrier UNRESOLVED."},{"id":"atlas:v16-48","status":"restricted","text":"v16.48, PR #96, merge 0c0efebe on research/v16.34-fiber-component-invariant, not main. Chain induction closed for every finite internal chain. Receipt cb086f9, workflow 36856450558, science VERIFIED. The older demo README still says PRE-CLOSURE. That is not the closure record. Arbitrary branching is not covered. This explains the chain bound. It does not select a source."},{"id":"atlas:v16-49","status":"restricted","text":"v16.49, PR #97, merge a8280c1, not main. FORK_CHAIN_INTERFACE_VALIDATED for one binary parent and two chain children. Closeout 9ffa81c approves CLOSED/CERTIFIED for that scope, terminal run 36863457271. Not arbitrary trees. Not a source."},{"id":"atlas:v16-50","status":"restricted","text":"v16.50, PR #98, merge 4a28661, not main. CLOSED/CERTIFIED for finite full binary trees: every internal has two children, not necessarily balanced. The total profile excursion stays at most 1 through repeated composition. Palette width is max(a,b) or a+b. The 1920 cases are directed checks, not an exhaustive census. The induction carries the general claim. Higher arity unresolved. Not a source."},{"id":"atlas:v16-51","status":"restricted","text":"v16.51, PR #99, merge 76f373c, not main. One ternary root over three full binary children, hitting number 2. TERNARY_Q2_INTERFACE_VALIDATED. 2592 directed cases, zero construction failures. Repeated ternary composition was still open. The missed RED timing is disclosed. Not a nonunit witness."},{"id":"atlas:v16-52","status":"restricted","text":"v16.52, PR #100, merge b6bf957, not main. Repeated binary and ternary composition. Total excursion at most 1. Not every profile has several components. Higher arity out. Not a nonunit certificate."},{"id":"atlas:v16-53","status":"restricted","text":"v16.53, PR #101, merge f6d4d79, not main. Reusable interface for internal arities 2, 3, and 4. 2863 records. Arity 5 and above stay out. The counts are not the theorem."},{"id":"atlas:v16-54","status":"restricted","text":"v16.54, PR #102, merge 496a403, not main. Floor-two endpoints are connected with hitting number in {q-1, q}. Not the global sum at most 1. Higher floors remain OPEN."},{"id":"atlas:v16-55","status":"restricted","text":"v16.55, PR #103, merge 3183c29, tip 0a1cd70, not main. Bounded R1–R5 renewable-guard repair. Run 37211847122 passed. Not universal X15U, X32, or X33. Not a source."},{"id":"atlas:a11-x59","status":"restricted","text":"A11.X59, research/uqcf-overlapping-guard-exchange, not main. Accepted analytical checkpoint on a colored carrier. Not a numbered v16 certificate. Not native disconnection. Not a source."},{"id":"atlas:a11-x60","status":"restricted","text":"A11.X60, same branch, not main. Every prescribed permutation inside the stated colored carrier has a direct {3, 4} minimum path. Not universal arbitrary-root repair. Not an obstruction to every temporary incidence."},{"id":"atlas:a11-x61","status":"restricted","text":"A11.X61, same branch, not main. Sufficient hybrid-boundary batch interface. Not three-cover necessity. X62–X64 have no closeout."},{"id":"atlas:a12","status":"restricted","text":"A12.1–A12.5, issue #104, commit bbc6e6f, not main. Self-contained closeout. Run 37502203890 passed. Not numbered v16 certification. Not physical validation. The stronger graph-descriptor impossibility is withdrawn as unproved, not declared false."},{"id":"atlas:post-a12","status":"restricted","text":"7 Oct index at 6a99418, not main. Auxiliary cycle breaking was the named next line then. The 10 Oct tip does not keep it as the frontier and does not publish a closeout under that name. Not a physical primitive. Not a source."},{"id":"atlas:c3-reserve","status":"restricted","text":"Tip 1e7cd09, not main. Spare labels can stay unreachable from a non-isolated source. Not a general impossibility. Static capacity is not connectivity. Not numbered v16. Not a source."},{"id":"atlas:c3-repair","status":"restricted","text":"Scoped repair interfaces, not main. Deficit, role-complete, shared-host, and a visible buffer. Not broad C3. Not guaranteed progress. Not numbered v16."},{"id":"atlas:c3-readout","status":"restricted","text":"Count reconstructions, not main. Miss counts and one-toggle inversion do not derive access. Safe core writes do not initialize the hidden record. Native origin stays open."}],"text":"Compiled 10 Oct 2026. Main STATUS.md is still the v15.44/v15.45 publication note. The v15.03 obstruction is not erased. Source correspondence NOT_EVALUATED. Pillar 3 OPEN. scientific_breakthrough: false. The integration branch is still v16.55, not on main. The overlapping-guard tip 1e7cd09 records scoped C3 and C4 closeouts. Spare capacity is not reachable reserve. That obstruction is not a general impossibility. Broad C3 and native record origin stay open. None of this is numbered v16 certification or a source.\n\nWhat changed\n\nv15.98 is no longer open. Two source actions can expose weight-four information that neither exposes alone. Overlapping sources also carry an order contrast. Disjoint sources commute and still activate both loops, with order contrast zero. That is COMPOSITION_ORDER_GEOMETRY_CONFIRMED and COMMUTING_COMPOSITION_ACTIVATION_CONFIRMED, commit 3a3655a. Not a selected physical law.\n\nv15.99 is INVALID. The native scaling and erasure predicates can look true and still do not override a failed rank-covariance control. There is no green scientific pass. v16.00 then records FROZEN_INPUT_RANK_RESIDUAL_PERSISTS: a readout-only recovery fails, and green CI accepts that NO. v16.01 and v16.02 recover specified comparisons at 50 and 80 digits. Complete erasure has an undefined polar, not an assigned rank of zero. v16.02 says the historical INVALID record is not rewritten.\n\nv16.03–v16.12 stay on the channel side. An attenuation placed between two commuting sources can carry order-dependent cubic information. That cubic factors. The null is localized off five edges and onto the sixth. The sixth edge is outside the inherited polar domain. Support-polar transport is discontinuous, including on physical paths that share a baseline. One-sided polar limits exist, and reversing the source coherence changes them. Keeping singular-value magnitude gives a continuous signed-normal observable. That does not make the old polar readout continuous, and it does not derive gravity.\n\nv16.13F restarts from v16.12 and stops short of a foundation. Retained lineage, pruning, and source pushforward close. Composition of the intrinsic obstruction does not. The missing typed object is a transport for obstruction information. The file says that object is not a metric, connection, curvature, quantum carrier, or gravity criterion. v16.14F makes the graded pieces canonical and the transport between them not canonical. v16.15F says a later obstruction still acts on distinctions lost earlier. v16.22 keeps a Green response as a reference and shows comparison diagrams do not force that inverse. v16.32 is NONINJECTIVE: the closure data do not reconstruct the indexed cover. v16.35 finds positive combinatorial barriers between some equivalent states. Those barriers are not energies, times, or geometric distances. v16.36 asks whether a local signature fixes them. Pair-completeness of the 18 records is certified. Gate D stays UNRESOLVED.\n\nv16.37 exhausts rooted trees of at most five vertices, with one, two, or three views: 51 graphs, 6325 states, 69 component pairs, 77 endpoint pairs, zero nonunit pairs. Outcome BOUNDED_UNIT_ONLY. v16.38 exhausts trees of at most six vertices: 111 graphs, 52907 states, 244 component pairs, 1497 endpoint pairs, zero nonunit pairs. Same outcome. The universal unit law stays UNRESOLVED. v16.39, commit c934fee, is an exploratory proof, not a new numerical campaign. If the saturation condition holds, endpoints in different components of the exact q-fiber have primary barriers and LEX_BARRIER equal to (1,1,1). Independent review calls that argument sound as a sufficient condition. It is not a characterization. A five-vertex nested restricted-support example still has a four-move unit path. Numbered-stage certification is pending.\n\nv16.40 through v16.48 stay on research branches. The object is a unit barrier: admitted paths may leave an exact profile, and the maximum L1 excursion on a repairing path is at most 1, inside a stated family. A figure that states this for every tree is ahead of the files. v16.40, one fixed tree, validates a moving deviation location. A single fixed coordinate is not enough for that pair. indecomposable_fixed_coordinate stays UNRESOLVED. It is not a smallest-witness theorem and not physical energy. v16.41 records a partition theorem on finite rooted no-unary trees with k equal to the leaf count and q equal to outdegree. Intrinsic indecomposability is NOT_CLAIMED. The finite remainder had zero nonunit pairs. v16.42 is FAMILY_THEOREM_VALIDATED for the reviewed T(d,m) family only: an m-leaf overlapping core behind d binary side branches. v16.43 classifies rooted stars with m and k at least 2. Exact hitting-number fibers are one component except the packed case m=k=q. Nested interactions stay UNRESOLVED. v16.44 covers every admitted no-unary rooted tree with exactly two internal vertices and k at least 2. Barriers between distinct exact components are 1. v16.45 is a family theorem, not one graph: every admitted no-unary rooted tree with exactly two root children, each the center of a star, at arbitrary leaf degrees and palette size in that domain. REPORT.md records BINARY_FORK_THEOREM_VALIDATED. Every state in an attained profile reaches a canonical state by single-label moves with total L1 deviation at most 1. Inside an exact component the barrier is 0. Between distinct exact components B1, Binf, and Bs are each 1. The family has three internal vertices. It does not cover three-internal chains, extra root children, arbitrary retained trees, or a physical evolution. Finite checks do not themselves prove the quantifiers. v16.46 is the non-saturated three-internal chain lemma. The saturated outer root was left UNRESOLVED at that gate. v16.47 includes the saturated outer root for every three-internal chain of degrees at least 2. Not arbitrary branching. v16.48 is compact-palette induction for every finite internal chain, total L1 excursion at most 1. PR #96 merged that record into research/v16.34-fiber-component-invariant as 0c0efebe. Receipt cb086f9 records workflow 36856450558 against that head, science VERIFIED. The demo README still contains the earlier PRE-CLOSURE sentence. That sentence does not erase the later closure. Arbitrary branching is not covered. Six-graph checks and directed constructions test the implementation. They are not the general proof. The universal unit barrier stays UNRESOLVED.\n\nHeight 1 does not mean the exact profile almost determines the component, and it does not mean one move. v16.43 is the counterexample. A packed star m=k=q has m! isolated exact-profile components, every pair at barrier 1. Ten leaves and ten labels are 3628800 components of one profile. The star proof exchanges two labels in four incidence moves, then composes those exchanges. The maximum excursion stays 1 through a long sequence. A constant barrier rules out only a proposal that lets source strength be a function of barrier height alone. It does not prove the retained structure is too dull to contribute. The chain induction is a positive explanation of why the bound holds for chains. It is not a negative chapter, and it is not P.\n\nv16.49 joins two internal-chain children under one binary parent. PR #97 merged as a8280c1. FORK_CHAIN_INTERFACE_VALIDATED. 133 normalizations, 192 directed cases, zero nonunit pairs. Frozen k=2 and k=3 graphs have 430250 states and 809 component pairs. Receipt 9d087af and closeout 9ffa81c approve CLOSED/CERTIFIED for that scoped theorem, terminal run 36863457271. An earlier README PRE-CLOSURE line is not that closeout. Arbitrary trees stay out. Do not score unit as failure or nonunit as success.\n\nv16.50 closes repeated binary composition, not another larger test. PR #98 merged as 4a28661. Full binary means every internal vertex has exactly two children. It does not mean balanced or uniform depth. A repaired child gives a fixed-root repair, a compact canonical endpoint, and label-role exchanges that keep its interior. Joining two children preserves those properties, so the argument repeats through any finite binary tree without raising the excursion bound. The bound is the total: the sum of absolute profile deviations over all vertices is at most 1. A one-unit difference at one vertex is not the result. There the hitting number is only 1 or 2, and the construction keeps separate deviations from coexisting. This is an existence theorem for a suitable sequence. It is not every sequence, not a short sequence, and not a selected evolution. The minimum palette width is necessary and sufficient: children of widths a and b require max(a,b) when the parent hitting number is 1, and a+b when it is 2. Overlap reuses labels. Disjoint children reserve separate labels. Those resources can grow while the peak departure stays 1. The uniform barrier is not the whole structure, and it is not merely a uniform tax. The 1920 directed cases, 72512 moves, and 994 checks support the implementation. They do not enumerate every state. The general claim rests on the induction. All 36 scientific files matched at the merge. The published closeout is CLOSED/CERTIFIED. An earlier REPORT.md line that receipt closeout remained required is not that closeout. Higher arity stays open. No nonunit counterexample is claimed.\n\nThe three-child question was then run, and it did not stay the frontier. v16.51, PR #99, merge 76f373c, is CLOSED/CERTIFIED under AMENDMENT_001 for one genuine ternary root over three arbitrary finite full binary children, centered on hitting number 2. Outcome TERNARY_Q2_INTERFACE_VALIDATED. 2592 directed identities, 864 with root target 2, 92352 primitive moves, zero construction failures. Repeated ternary composition was still out of scope. The missed preimplementation RED timing is disclosed and is not claimed after the fact. The pairwise-overlap pattern was the interface, not a nonunit witness. v16.52, PR #100, merge b6bf957, repeats that interface through binary and ternary composition for finite ordered rooted trees in the stated nested-support category. Total excursion at most 1. Barriers 0 inside an exact component and 1 between distinct exact components. It does not say every profile has several components. 7236 directed cases. Higher arity stayed out. v16.53, PR #101, merge f6d4d79, extends the reusable interface to internal arities 2, 3, and 4. 2863 records and 34234 moves support the implementation. They are not the theorem. Arity 5 and above stay outside. v16.54, PR #102, merge 496a403, is a different statement. For arbitrary feasible arity and target q at least 3, exact-q endpoints whose root floors are all 2 are connected by a path whose hitting number stays in {q-1, q}. That is floor-two parent-support connectivity. It is not the global sum at most 1. Higher-floor connectivity remains OPEN. v16.55, PR #103, merge 3183c29, with later reporting acceptance at 0a1cd70, is CLOSED/CERTIFIED for a bounded R1–R5 renewable-guard repair and conditional native integration. Actual-merge run 37211847122 passed. Protected degree leveling, saturated reusable exchanges, multiple-patch placement, and original-grade guards keep completed lower paths in the one-unit band and restore the declared endpoints. Universal X15U root repair, and X32 and X33, are not this certificate. No mixed-floor, higher-target, or unrestricted nested result is claimed. The integration branch did not move after that tip.\n\nNew work after that tip is on research/uqcf-overlapping-guard-exchange, still not on main. On 5 Oct 2026, A11.X59, A11.X60, and A11.X61 were accepted as analytical checkpoints, not as numbered v16 certificates. X59 and X60 stay inside a colored carrier. X60 says every prescribed role permutation in that carrier has a direct path in the hitting band {3, 4} at the global endpoint Hamming minimum. It is not universal arbitrary-root minimum repair. A control in which every minimum-incidence path uses at least three four-covers is an all-minimum-path bound for that control. It is not an obstruction to every temporary incidence. X61 is a sufficient hybrid-boundary batch interface on stated exact-four endpoints. Three-cover necessity is not claimed. X62 and X63 have scopes only. X64 is a cycle-breaking slack candidate, corrected before a proof. None of those three has a closeout. On 6 Oct 2026 issue #104 closed A12.1–A12.5 at commit bbc6e6f for the corrected statements: written mathematics, an author-side audit, and bounded verification run 37502203890. That is not independent peer review, not a proof assistant, not numbered v16 certification, and not physical validation. A12.2 keeps the family count n+3 and withdraws, as unproved, the stronger claim that the labelled pairwise response graph cannot be a complete state descriptor. That withdrawal is not a declaration that the claim is false. A12.5 says the stated L and I inputs cannot determine exact legality. It does not exclude every locality notion. Failed RED runs 37500570046 and 37500792495 stay in the record. No A12.6. Certified v16.54 and v16.55 are unchanged. On 7 Oct 2026 the same branch tip 6a99418 records scoped analytical closeouts after A12, through a joint event cycle that uses a temporary bypass. These are written scoped proofs, not numbered certificates. The full B1/B2 program is not closed. The next obligation at that 7 Oct commit was auxiliary cycle breaking. The 10 Oct tip does not publish a closeout under that name and does not keep it as the frontier. None of this is a source.\n\nOn 10 Oct 2026 the same branch tip is 1e7cd09. Main STATUS.md is still the v15.44/v15.45 publication note. CI commits on main are review workflows, not a science publication. The index records scoped C3 and C4 closeouts. They are not numbered v16 certificates and not a full-stack certification. Static capacity is exact in its domain and is not connectivity. An isolated source can have spare labels that no safe toggle reaches. A later source is not isolated: safe edits exist, and the uniformly safe component still has exactly seven cores, so the spare labels stay unreachable for n at least 3. Kappa below the palette size, plus unrelated local progress, is not a transferable-reserve criterion. It is not a general impossibility theorem. Universal core region means admissible for every original protected hidden completion in the declared tau 3 to 4 domain. It does not give observer access. Repair interfaces in the same index, including deficit, role-complete, shared-host, and a visible buffer, are scoped. They do not give guaranteed progress or broad C3. Count reconstructions, including miss counts through 15 roots and one-toggle support inversion, do not derive field access. Uniformly safe core writes do not initialize the hidden record. Native record origin, broad C3, and general C4 stay open. The named next task is a restoring path for one prescribed occupied label. Archived Gemini reviews accepted scoped writeups. That is not peer review and not a source. No force, geometry, energy, or gravity is claimed.\n\nv15.98, research/v15.98-composed-four-body-response, commit 3a3655a, not merged. COMPOSITION_ORDER_GEOMETRY_CONFIRMED and COMMUTING_COMPOSITION_ACTIVATION_CONFIRMED. Four-body exposure does not require noncommutation. Order contrast is a separate measurement. Not gravity.\n\nv15.99, research/v15.99-intermediate-eb-retention, not merged. Both preregistered verdicts are INVALID. Rank covariance failed. Predicates that evaluate true do not override validity. Not a certified physical result.\n\nv16.13F, not merged. RETAINED_FOUNDATION_PARTIALLY_CLOSED_WITH_TYPED_BOUNDARY and INTRINSIC_OBSTRUCTION_COMPOSITION_UNDERDETERMINED. The missing object is obstruction transport. Not a metric, not a quantum carrier, not Einstein. scientific_breakthrough: false.\n\nv16.32, not merged. NONINJECTIVE. The value-level closure earned through v16.31 does not reconstruct the underlying indexed retained cover. Smallest witness: three vertices, two views.\n\nv16.35, research/v16.35-fiber-barrier-closure, not merged. Eighteen pairs of consistency-equivalent retained states have a positive exact barrier: every legal one-incidence path must leave the endpoint quotient. The barrier coordinates are not energies, times, or geometric distances.\n\nv16.36 RESULTS.md, frozen at merge ce4f0c0 on research/v16.34-fiber-component-invariant, 30 Sep 2026, not on main. Gates A and B CLOSED. Gate C is BOUNDED NO-COLLISION. Gate D is UNRESOLVED. LOCAL_UNIT is not claimed. Gate E is not a universal ultrametric theorem. The earlier verifier recomputed each supplied pair and did not independently prove that all 18 required pairs were present. PR #80 (d887068) added the P1–P8 proof ledger and did not close that gap. PR #81 enumerates the canonical universe, requires exact record equality, and rejects omissions, duplicates, and same-count substitutions. Post-merge audit 36731692842, workflow head 8941af1, froze ce4f0c0, reconstructed 18 records, and passed the inherited stack. No scientific conclusion changed. Signature C uses attainable tau on the minimax-feasible subgraph, so it still depends on the certified barrier and is not an independent predictive law. Next obligation, not a result: prove that factorization in general, or find a counterexample.\n\nv16.37, research/v16.37-certified-closure, not on main. Every rooted unordered tree with 1–5 vertices and k in {1,2,3}: 51 graphs, 6325 states, 77 endpoint pairs, zero nonunit pairs. BOUNDED_UNIT_ONLY. Universal unit law UNRESOLVED. Audit receipt e5c3e33.\n\nv16.38, merge e4de671, not on main. Every rooted unordered tree with 1–6 vertices and k in {1,2,3}: 111 graphs, 52907 states, 1497 endpoint pairs, zero nonunit pairs. BOUNDED_UNIT_ONLY. Universal unit law UNRESOLVED. Audit receipt ed87aef.\n\nv16.39, commit c934fee, not on main. Sufficient saturation condition for unit barriers, independently reviewed as sound. Not preregistered. No new numerical execution. Not a characterization. Not numbered-stage certified.\n\nv16.40, research/v16.40-coordinate-obstruction, not on main. One fixed tree. MOVING_LOCATION_WITNESS_VALIDATED: a unit path whose deviation coordinate changes. A single fixed coordinate is not enough for that pair. indecomposable_fixed_coordinate UNRESOLVED. Not a smallest-witness theorem. Not physical energy. Universal unit barrier UNRESOLVED.\n\nv16.41, research/v16.41-unit-barrier-dichotomy, not on main. PARTITION_THEOREM_VALIDATED_BOUNDED_REMAINDER_UNIT for partition profiles on finite rooted no-unary trees with k equal to the leaf count and q equal to outdegree. Intrinsic indecomposability NOT_CLAIMED. Finite remainder had zero nonunit pairs. Universal unit barrier UNRESOLVED.\n\nv16.42, research/v16.42-overlapping-core-repair, not on main. FAMILY_THEOREM_VALIDATED for the reviewed T(d,m) family only. Intrinsic indecomposability is not claimed. Universal unit barrier UNRESOLVED.\n\nv16.43, research/v16.43-star-fiber-classification, not on main. STAR_CLASSIFICATION_VALIDATED: exact hitting-number fibers of a rooted star with m and k at least 2 are one component, except the packed case m=k=q. The packed case has m! isolated components of one profile, every pair at barrier 1. Height 1 is not one component and not one move. Nested interactions UNRESOLVED.\n\nv16.44, research/v16.44-two-branch-unit-barrier, not on main. TWO_BRANCH_THEOREM_VALIDATED for every admitted no-unary rooted tree with exactly two internal vertices and k at least 2. Barriers are 1 between distinct exact components. Universal unit barrier UNRESOLVED.\n\nv16.45, research/v16.45-binary-fork-unit-barrier, not on main. Family theorem, not one graph: every admitted binary root with two star children, arbitrary leaf degrees and palette size in that domain. Total L1 at most 1. Barrier 0 inside an exact component. B1, Binf, and Bs are each 1 between distinct exact components. Chains, extra root children, and arbitrary trees stay out. Not a physical evolution.\n\nv16.46, research/v16.46-nested-chain-repair, not on main. NON_SATURATED_CHAIN_LEMMA_VALIDATED when the outer target is strictly below its degree. The saturated outer root was left UNRESOLVED at this gate. Universal unit barrier UNRESOLVED.\n\nv16.47, research/v16.47-saturated-chain-repair, not on main. THREE_INTERNAL_CHAIN_THEOREM_VALIDATED: every three-internal-vertex chain of degrees at least 2 and k at least 2 admits total L1 excursion at most 1, including the saturated outer root. Not arbitrary branching. Universal unit barrier UNRESOLVED.\n\nv16.48, PR #96, merge 0c0efebe on research/v16.34-fiber-component-invariant, not main. Chain induction closed for every finite internal chain. Receipt cb086f9, workflow 36856450558, science VERIFIED. The older demo README still says PRE-CLOSURE. That is not the closure record. Arbitrary branching is not covered. This explains the chain bound. It does not select a source.\n\nv16.49, PR #97, merge a8280c1, not main. FORK_CHAIN_INTERFACE_VALIDATED for one binary parent and two chain children. Closeout 9ffa81c approves CLOSED/CERTIFIED for that scope, terminal run 36863457271. Not arbitrary trees. Not a source.\n\nv16.50, PR #98, merge 4a28661, not main. CLOSED/CERTIFIED for finite full binary trees: every internal has two children, not necessarily balanced. The total profile excursion stays at most 1 through repeated composition. Palette width is max(a,b) or a+b. The 1920 cases are directed checks, not an exhaustive census. The induction carries the general claim. Higher arity unresolved. Not a source.\n\nv16.51, PR #99, merge 76f373c, not main. One ternary root over three full binary children, hitting number 2. TERNARY_Q2_INTERFACE_VALIDATED. 2592 directed cases, zero construction failures. Repeated ternary composition was still open. The missed RED timing is disclosed. Not a nonunit witness.\n\nv16.52, PR #100, merge b6bf957, not main. Repeated binary and ternary composition. Total excursion at most 1. Not every profile has several components. Higher arity out. Not a nonunit certificate.\n\nv16.53, PR #101, merge f6d4d79, not main. Reusable interface for internal arities 2, 3, and 4. 2863 records. Arity 5 and above stay out. The counts are not the theorem.\n\nv16.54, PR #102, merge 496a403, not main. Floor-two endpoints are connected with hitting number in {q-1, q}. Not the global sum at most 1. Higher floors remain OPEN.\n\nv16.55, PR #103, merge 3183c29, tip 0a1cd70, not main. Bounded R1–R5 renewable-guard repair. Run 37211847122 passed. Not universal X15U, X32, or X33. Not a source.\n\nA11.X59, research/uqcf-overlapping-guard-exchange, not main. Accepted analytical checkpoint on a colored carrier. Not a numbered v16 certificate. Not native disconnection. Not a source.\n\nA11.X60, same branch, not main. Every prescribed permutation inside the stated colored carrier has a direct {3, 4} minimum path. Not universal arbitrary-root repair. Not an obstruction to every temporary incidence.\n\nA11.X61, same branch, not main. Sufficient hybrid-boundary batch interface. Not three-cover necessity. X62–X64 have no closeout.\n\nA12.1–A12.5, issue #104, commit bbc6e6f, not main. Self-contained closeout. Run 37502203890 passed. Not numbered v16 certification. Not physical validation. The stronger graph-descriptor impossibility is withdrawn as unproved, not declared false.\n\n7 Oct index at 6a99418, not main. Auxiliary cycle breaking was the named next line then. The 10 Oct tip does not keep it as the frontier and does not publish a closeout under that name. Not a physical primitive. Not a source.\n\nTip 1e7cd09, not main. Spare labels can stay unreachable from a non-isolated source. Not a general impossibility. Static capacity is not connectivity. Not numbered v16. Not a source.\n\nScoped repair interfaces, not main. Deficit, role-complete, shared-host, and a visible buffer. Not broad C3. Not guaranteed progress. Not numbered v16.\n\nCount reconstructions, not main. Miss counts and one-toggle inversion do not derive access. Safe core writes do not initialize the hidden record. Native origin stays open.\n\nv15.98 RESULTS.md\nv16.13F RESULTS.md\nv16.35 RESULTS.md\nv16.36 RESULTS.md at ce4f0c0\nPR #81 pair-completeness\nPR #80 proof ledger\nv16.37 REPORT.md\nv16.38 REPORT.md\nv16.39 structural theorem\nv16.40 REPORT.md\nv16.45 REPORT.md\nv16.48 PR #96 closure\nv16.48 receipt cb086f9\nv16.49 closeout 9ffa81c\nv16.50 PR #98\nv16.51 PR #99\nv16.52 PR #100\nv16.53 PR #101\nv16.54 PR #102\nv16.55 PR #103\n10 Oct synthesis at 1e7cd09\nLocal-progress closeout\nA12 issue #104\nA12 closeout bbc6e6f\nPost-A12 synthesis 6a99418\nv15.55 RESULTS.json\nv15.78–v15.97\nLive gates","howToCite":"Spradlin, A. (2026-10-10). v15.98 through v16.55, then A12. Retained Atlas. https://aaronspradlin.grok.me/wiki/v1598-line. Keep claim badge: restricted."}