Pith Number

pith:YMVAX5YW

pith:2012:YMVAX5YWV2KP4D4C5CHRGYA5LT

not attested not anchored not stored refs pending

Homotopy invariance through small stabilizations

Beatriz Abadie, Guillermo Corti\~nas

arxiv:1212.5901 v3 · 2012-12-24 · math.KT · math.OA · math.RA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YMVAX5YWV2KP4D4C5CHRGYA5LT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T02:57:06.824989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c32a0bf716ae94fe0f82e88f13601d5ceb0929360e30368a7baf2759531d1460

Aliases

arxiv: 1212.5901 · arxiv_version: 1212.5901v3 · doi: 10.48550/arxiv.1212.5901 · pith_short_12: YMVAX5YWV2KP · pith_short_16: YMVAX5YWV2KP4D4C · pith_short_8: YMVAX5YW

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/YMVAX5YWV2KP4D4C5CHRGYA5LT \
  | 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: c32a0bf716ae94fe0f82e88f13601d5ceb0929360e30368a7baf2759531d1460

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6112dc2e99a9b704d043b95725f2e78704356023c9e71e6d014a9b690b93f287",
    "cross_cats_sorted": [
      "math.OA",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-12-24T12:19:48Z",
    "title_canon_sha256": "dcae7fe4cb81462b047e290552f5ef97adec43896d4984430dc6ceda89f4b286"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5901",
    "kind": "arxiv",
    "version": 3
  }
}