Eight Postulates, One Core Sample Each

Computed live below by simple average across all eight postulates' segment data — not a literal document metric. STATUS-TAG CHANGE, v43: Postulate 6/8's “which 4 of 7” generator-assignment question is upgraded from CONJECTURE/OPEN to DERIVED (Addendum GQ, an exact proof via Cayley-Dickson doubling, not numerical evidence) — the aggregate above reflects this. v41–v42 (Addenda GE–GN) advanced the H.17/AZ.13 decoupling and Postulate-3 literal-coefficient threads with no formal status-tag changes. v44 (Addenda GR–GU) generalizes the H.17 nucleation mechanism to a third construction, tests four external escape routes proposed by outside collaborators (all four negative), proves G2 has no invariant fixed direction on any construction (unifying four earlier failed attempts as one fact), and corrects a substrate-naming mix-up affecting Postulate 7's AZ.13 discharge-mechanism entry (see P7) — no formal status-tag changes that round. v45 (Addenda GV–HC, eight addenda) settles H.17's own six-construction plateau puzzle after a 121-hour computation reaching N=261,815: the outlier construction genuinely plateaus, confirming the earlier claim but at a materially lower value (est. 1.5–1.7%, not 2.05–2.39%); three further hypotheses for its uniqueness (nilpotency class, center ratio, derived-subalgebra ratio) are excluded across a seventh tested construction; a second, symmetry-based obstruction axis is identified alongside GT's counting-based one; and three more candidate escapes (causal-set order theory, BFSS Matrix Theory, nonlocal fermionization) are tested and closed. Separately, Postulate 7's AZ.13 entry gets a correction-in-place: the GR anisotropy figure (0.386) is found not scale-invariant, climbing across tested radii rather than settling — flagged open, not reversed (see P7). No formal status-tag changes this round either. v46 (Addenda HD–HF) runs the most thorough sweep yet on why H₁(ℤ) uniquely plateaus — eight constructions and six candidate discriminators now excluded, still unexplained — and closes all four externally-proposed H.17-resolution mechanisms (two were already closed elsewhere in the record, unknown to the proposing survey; two closed on direct test); separately backfills a previously-lost eight-addendum thread (Addenda AA–AH, recovered from a 2026-07-17 session, cited by letter in three later addenda with nothing behind the citation until now). v47 is documentation-only, no new physics: restores an early Master Document snapshot (Part III §G) and a further nine addenda (AO–AX, 2026-07-18/19), and closes the companion Addenda Archive's own long-standing Contents-index gap. v48 (Addenda HG–HJ) tests H.17's long-flagged "fifth paradigm" — an associator-directed accretion walk — still log-diameter, an eighth independent construction landing in that class; closes off a potential fourth literal-coefficient candidate for Postulate 3 via a new exact identity and a Schur's-lemma proof (the three-way underdetermination itself remains exactly as open as before); and applies a conductance diagnostic to that same construction, sharpening rather than reproducing an earlier bottleneck finding — a ninth independent construction sharing the log-diameter default. v49 (Addenda HK–HM) closes the entire static-scalar-invariant approach to H.17's adjacency question by representation theory (not just another negative construction), and survives a deliberately harder stress test of the architect's own Q=4 (Bass–Guivarc'h) lead — catching and fixing a real toolkit embedding bug along the way. v50 (Addenda HN–HP) closes a second, independent route to Postulate 3's three-way coefficient question (also negative), narrows rather than resolves the Q=4 discriminator search across four tested mechanisms, and closes two v33-era follow-up questions on the theory's speed-of-light derivation. No formal status-tag changes across v46–v50. H.17 remains CONJECTURE/OPEN, PERMANENT ENTRY. v51 (Addenda HQ, HR, HS) conducts an exhaustive discontinuity search for GR.24, directly executing HO's own flagged next step: computing automorphism Lie algebras from scratch for every construction in the theory's test family, then locating and applying a complete classification theorem (Saldarriaga et al.) proving all Heisenberg-type parabolic nilradicals of any simple Lie algebra reduce to exactly two finite families indexed by ℝ, ℂ, ℍ, 𝕆 — HQ finds exactly two survivors of every filter identified: H₁(ℤ) itself (already confirmed to plateau) and a previously untested construction, 𝔥₁(ℂ) (structure group GL(2,ℂ), no property (T), algebraically one level up from H₁(ℤ)'s own GL(2,ℝ)). Separately, HR resolves standing conjecture AY.4 — whether R/S/T can rescue Addendum AU's chiral rotating-wave state the same way they rescue the real fixed point: an exact symbolic proof shows R and T cannot, for any coupling strength; S is closed to the same conclusion by broad numerical closure (3,259/3,259 configurations). AY.4 moves CONJECTURE → DERIVED (false for R/T, strongly evidenced false for S) — the chiral state is structurally harder to stabilize than the real fixed point. HS then builds HQ's flagged 𝔥₁(ℂ) construction and runs it across six radii (N=6,653 to 1,072,837, a 161× range): peak swing stays flat throughout (0.907%–1.443%), consistent with H₁(ℤ) and 𝔥₁(ℂ) sharing the same dynamical status, though at a lower plateau band (0.9–1.4% vs. 1.5–1.7%) and short of Addendum HC's own monotonic-collapse rigor. GR.24's algebraic exhaustiveness question is now closed; no mechanism explaining the plateau itself has been found. No formal status-tag changes this consolidation (AY.4 is a sub-postulate item within Postulate 3). Also this consolidation: the Addenda Archive's GZ/HA/HB heading-format bug is fixed and GZ's three previously-dropped data tables are restored; the Master Document's front-matter Documentation Notes section is relocated to the end of the document. v52 (Addenda HT, HU, HV) pushes the new candidate's dynamical test one radius further — the single longest continuous computation in the project's history — and the flat pattern holds at this larger scale too; a companion correction retracts the inference drawn from an earlier measurement about which case is the minimal example of this construction type, though the measurement itself stands (HT). A literature review finds a second, independent classification axis that disagrees with the newer construction's own name, and corrects the citation for the classification theorem applied at v51 from “Saldarriaga et al.” to its actual authors, Kaplan & Subils (HU). A direct search for the mechanism behind the plateau tests five literature-informed hypotheses and rules out all five (HV). No formal status-tag changes this consolidation. Aggregate bar unchanged from v51, confirmed by recomputation since no postulate status tags changed. NEW AT V53 (Addenda HW–IB, six addenda): a search that had produced five straight negative results finally gets a positive one. A test built specifically to confirm or kill one hypothesis about why a single construction behaves differently from every other one tried comes back confirming it — the pattern decays exactly as predicted, pointing to a specific structural property as the actual cause (HY). The same round closes a sixth negative statistic on the same question (HX) and a third, independently-derived negative route on a separate long-open coefficient question (HW). Separately, a discharge condition previously confirmed on only one kind of substrate is now shown to hold unconditionally on two more (HZ, IA), and a deliberate attempt to find a substrate where it fails instead turns up a clean mathematical rule for when it gets harder to trigger, tested across six orders of magnitude with no floor found yet (IB). No formal status-tag changes anywhere in the theory this consolidation. Aggregate bar unchanged from v52, confirmed by recomputation since no postulate status tags changed.