Pith Number

pith:G72U46KJ

pith:2026:G72U46KJNUMEXRFEMUSA3GEDK7

not attested not anchored not stored refs pending

Cells, convexity and contractibility in general categories

Suddhasattwa Das

Categories obeying basic axioms admit convex contractible cells whose maps reconstruct homology and homotopy.

arxiv:2604.16126 v3 · 2026-04-17 · math.CT

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\usepackage{pith}
\pithnumber{G72U46KJNUMEXRFEMUSA3GEDK7}

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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

✓ Portable graph bundle live · download bundle · merged state

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

In any category satisfying a short list of axioms, one can construct cells that are convex and contractible in the categorical sense, and the maps from objects into these cells determine the homology and homotopy of the category.

C2weakest assumption

The category obeys a small collection of axioms that are sufficient to guarantee the existence of the required cells and the reconstruction of homology and homotopy from maps into them.

C3one line summary

Cells with convexity and contractibility can be built inside any category satisfying a short list of axioms, and the resulting cell data suffice to define homology and homotopy.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T01:03:47.152004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37f54e79496d184bc4a465240d988357ea2394d2a0abb042b35f12dabeb63d2a

Aliases

arxiv: 2604.16126 · arxiv_version: 2604.16126v3 · doi: 10.48550/arxiv.2604.16126 · pith_short_12: G72U46KJNUME · pith_short_16: G72U46KJNUMEXRFE · pith_short_8: G72U46KJ

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/G72U46KJNUMEXRFEMUSA3GEDK7 \
  | 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: 37f54e79496d184bc4a465240d988357ea2394d2a0abb042b35f12dabeb63d2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dbce172b152f2b5626b5f36c75760e928b6ff95c0fc6bfa66e81fa92e2e5e6f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-04-17T15:00:21Z",
    "title_canon_sha256": "961fd3ba231626f3c46b837aab714a88d0f6b3a112c475e5fe395ce0708be729"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.16126",
    "kind": "arxiv",
    "version": 3
  }
}