Pith Number

pith:7CG4LCJ7

pith:2011:7CG4LCJ7PDM2PBAM52YOBQOSWB

not attested not anchored not stored refs pending

Whitney categories and the Tangle Hypothesis

Conor Smyth, Jon Woolf

arxiv:1108.3724 v1 · 2011-08-18 · math.CT · 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{7CG4LCJ7PDM2PBAM52YOBQOSWB}

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	2026-05-18T04:15:07.586865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f88dc5893f78d9a7840ceeb0e0c1d2b0750f5e13076c67ea37168393deac24b8

Aliases

arxiv: 1108.3724 · arxiv_version: 1108.3724v1 · doi: 10.48550/arxiv.1108.3724 · pith_short_12: 7CG4LCJ7PDM2 · pith_short_16: 7CG4LCJ7PDM2PBAM · pith_short_8: 7CG4LCJ7

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/7CG4LCJ7PDM2PBAM52YOBQOSWB \
  | 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: f88dc5893f78d9a7840ceeb0e0c1d2b0750f5e13076c67ea37168393deac24b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "464ed2346cd1a978fbf8662c11339d0fda7d4aeab35d099e78f2ee2ac0743f28",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2011-08-18T11:34:08Z",
    "title_canon_sha256": "2b0eb388944962cbc38f30f4057ec59457bd25e1caa516a62d40ed4c873f0ded"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3724",
    "kind": "arxiv",
    "version": 1
  }
}