Pith Number

pith:BVTAVZV2

pith:2026:BVTAVZV23TIJ76PY45XMD4D2L7

not attested not anchored not stored refs pending

A categorical and algebro-geometric theory of localization

Mauricio Corr\^ea, Simone Noja

Localization for theories with open-closed recollements produces a torsor of supported refinements on the closed locus rather than a single distinguished class.

arxiv:2604.03845 v3 · 2026-04-04 · math.AG · math-ph · math.DG · math.GT · math.MP

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\usepackage{pith}
\pithnumber{BVTAVZV23TIJ76PY45XMD4D2L7}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Starting from a class on a space whose restriction to the open complement vanishes, we show that the natural output of the formalism is, in general, not a distinguished localized class on the closed locus, but rather a torsor of supported refinements; a canonical local term arises only once an additional uniqueness or concentration principle is imposed.

C2weakest assumption

The existence of an open-closed recollement together with the additional uniqueness or concentration principle needed to select a canonical local term from the torsor; without it the output remains a torsor rather than a single class.

C3one line summary

Localization in recollement-equipped cohomological theories naturally produces a torsor of supported classes; a unique local term requires extra concentration or uniqueness assumptions, and the setup recovers standard Euler formulas under purity.

Receipt and verification

First computed	2026-06-23T03:13:56.942388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d660ae6badcd09ff9f8e76ec1f07a5ff1a6b5db1f9f8608a30917cd1beb3edb

Aliases

arxiv: 2604.03845 · arxiv_version: 2604.03845v3 · doi: 10.48550/arxiv.2604.03845 · pith_short_12: BVTAVZV23TIJ · pith_short_16: BVTAVZV23TIJ76PY · pith_short_8: BVTAVZV2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BVTAVZV23TIJ76PY45XMD4D2L7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0d660ae6badcd09ff9f8e76ec1f07a5ff1a6b5db1f9f8608a30917cd1beb3edb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95816881a48771c2f2cb93533fad73ccf6d035477b47dd59921aa1b14c395313",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.GT",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-04T20:00:45Z",
    "title_canon_sha256": "fcf538944dd5660fdbfaba07c9beb4de7a2ec5ac1c72e4b9e21fdfa635a81644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03845",
    "kind": "arxiv",
    "version": 3
  }
}