# Attractive Centers - Version 2

Published 1 October 2026, separately named `_v2.pdf`. The originals have NOT
been overwritten or deleted. The website offers both editions.

## Revisions

- I: B46 as an inner comparison; standard chest and four-point outer theory
  retain their earlier scope. No OSC or maximal-Heart claim.
- II: dated historical ETC experiment, current evidence classes and the
  relationship of global containment to the unresolved extension problem.
- III: the two strict power-endpoint exposure witnesses, exact rational
  directions, and residual/strong-convexity root-error certification. The
  universal power interval remains unchanged.
- IV: all 46 generators, fixed-B76 hull equality, minimum-subset bounds
  44-46 within that fixed reference, the universal containment audit of all
  1,142 currently proved native maps, reproducibility architecture, current
  numerical statuses and a freshly calculated 13-20-21 diagnostic figure.

R44 means B46 without the two powers; it is NOT the proposed B44 reduction.
Proposed B44 retains the powers and deletes F(-1/3,X2255) and X3794; universal
sufficiency is still unproved. B46 is neither asserted minimum nor maximal.
The rational analytic and power-inclusive continuous attractive classes are
distinguished. The new audit independently replays containment and source
normalization, but inherits the earlier native attractivity certificates.

The 1,142 entries are the current proved-native inventory, not a complete
classification of the ETC. The 2,613 additional numerical candidates and
514 unresolved high-range first-pass cases remain separately labelled.

## Preservation checks

All earlier PDF SHA-256 hashes were checked before publication:

| Paper | Preserved earlier PDF SHA-256 |
| --- | --- |
| I | `c746d6c97fd78996bbcc2528f9c7580405f87d8448520d864fd45001dec2f44c` |
| II | `f304685f064dee8ea1af99e53890826c2748382a0603ccfbaaf93af50a9adf03` |
| III | `5e87be5bdeedf6b64a2cba55986282b349a86b8c05bc20351545e29d99e96d32` |
| IV | `7f6ba66b46f1813ee5413142d8dbac147b71767d4e627c5cf19930fb4ec3cc3e` |

`VERSION_2_MANIFEST.json` records both old and new PDF hashes and page counts.
Every new page was rendered and inspected; sources compiled with TeX Live
2026 with no unresolved citations/references or overfull boxes.

The already-published versioned certificate deposit is unchanged:
[B46 proof handoff](explorer/B46-proof-handoff.zip).
Its SHA-256 is
`2e4a05d532d4141bfaab9fd21a471b064757a72a9a4957f6aca89ca81946db18`.