Pith Number

pith:GAKIHCAS

pith:2011:GAKIHCASQHMC25CE5FQRIZZBSS

not attested not anchored not stored refs pending

Commuting Groups and the Topos of Triads

Thomas M. Fiore, Thomas Noll

arxiv:1102.1496 v2 · 2011-02-08 · math.GR · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GAKIHCASQHMC25CE5FQRIZZBSS}

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	2026-05-18T04:26:12.749812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

301483881281d82d7444e96114672194b28c97465db31f5f2ab3a33ca574d106

Aliases

arxiv: 1102.1496 · arxiv_version: 1102.1496v2 · doi: 10.48550/arxiv.1102.1496 · pith_short_12: GAKIHCASQHMC · pith_short_16: GAKIHCASQHMC25CE · pith_short_8: GAKIHCAS

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/GAKIHCASQHMC25CE5FQRIZZBSS \
  | 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: 301483881281d82d7444e96114672194b28c97465db31f5f2ab3a33ca574d106

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f482c1509182342ba3bb8165f661699113e69cf7fcf46edad87d2697c1ba0e2f",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-02-08T03:47:13Z",
    "title_canon_sha256": "61bd561b77d8fea11eae1ed851d883cbca2289f5079a8752a4878d4148c1f856"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1496",
    "kind": "arxiv",
    "version": 2
  }
}