Pith Number

pith:7APG6SKX

pith:2010:7APG6SKXS5UNWVHB2PW2J3QIPW

not attested not anchored not stored refs pending

Group Width

Michael H. Freedman

arxiv:1011.2460 v2 · 2010-11-10 · 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{7APG6SKXS5UNWVHB2PW2J3QIPW}

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	2026-05-18T04:33:26.676470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f81e6f49579768db54e1d3eda4ee087dbbe9852ca21d7dfeb1db4f966a048fa1

Aliases

arxiv: 1011.2460 · arxiv_version: 1011.2460v2 · doi: 10.48550/arxiv.1011.2460 · pith_short_12: 7APG6SKXS5UN · pith_short_16: 7APG6SKXS5UNWVHB · pith_short_8: 7APG6SKX

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/7APG6SKXS5UNWVHB2PW2J3QIPW \
  | 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: f81e6f49579768db54e1d3eda4ee087dbbe9852ca21d7dfeb1db4f966a048fa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3b4aae855753214c3ff33ff0f00580e2bc3699c463db0d9822d01414f1e8cca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-11-10T19:13:12Z",
    "title_canon_sha256": "d64910a31cc2a10080f207f9b54a9b742d505d22ef6c22091905b3ac8e5a0dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2460",
    "kind": "arxiv",
    "version": 2
  }
}