Pith Number

pith:ODQEQ5VW

pith:2012:ODQEQ5VWPYCJ5BFKPW2POGULRZ

not attested not anchored not stored refs pending

Homotopical Intersection Theory, III: multi-relative intersection problems

Bruce Williams, John R. Klein

arxiv:1212.4420 v4 · 2012-12-18 · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ODQEQ5VWPYCJ5BFKPW2POGULRZ}

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	2026-05-17T23:45:00.605021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70e04876b67e049e84aa7db4f71a8b8e4360322eb9860e73e2e9a11753d0868f

Aliases

arxiv: 1212.4420 · arxiv_version: 1212.4420v4 · doi: 10.48550/arxiv.1212.4420 · pith_short_12: ODQEQ5VWPYCJ · pith_short_16: ODQEQ5VWPYCJ5BFK · pith_short_8: ODQEQ5VW

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/ODQEQ5VWPYCJ5BFKPW2POGULRZ \
  | 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: 70e04876b67e049e84aa7db4f71a8b8e4360322eb9860e73e2e9a11753d0868f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cd6241c3d3620cde4dd4c6a8fa217cfaa83b71b2e21e012f776c47f4185b88e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-12-18T16:43:38Z",
    "title_canon_sha256": "23bca515e7c5ed125e63e4fcd77bd1858826fbdac4ddd8ec6b65f07c8af6650e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4420",
    "kind": "arxiv",
    "version": 4
  }
}