Pith Number

pith:KDWGVXN7

pith:2011:KDWGVXN74DIOALQSOB5XTHZY65

not attested not anchored not stored refs pending

Homotopically trivializing the circle in the framed little disks

Gabriel C. Drummond-Cole

arxiv:1112.1129 v2 · 2011-12-06 · math.AT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KDWGVXN74DIOALQSOB5XTHZY65}

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	2026-05-18T00:44:30.499792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50ec6addbfe0d0e02e12707b799f38f749e039a77f321d335823c05c8893c89d

Aliases

arxiv: 1112.1129 · arxiv_version: 1112.1129v2 · doi: 10.48550/arxiv.1112.1129 · pith_short_12: KDWGVXN74DIO · pith_short_16: KDWGVXN74DIOALQS · pith_short_8: KDWGVXN7

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/KDWGVXN74DIOALQSOB5XTHZY65 \
  | 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: 50ec6addbfe0d0e02e12707b799f38f749e039a77f321d335823c05c8893c89d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d738a0bc79b703f313aa5d772c2c2f01af3ce1b9e207ec14f9324d865f236e29",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-12-06T00:21:18Z",
    "title_canon_sha256": "fb0fcf8c5da2ad8403e3b07c650c9531491b815b9a4f12921f6102ee05bad642"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1129",
    "kind": "arxiv",
    "version": 2
  }
}