Pith Number

pith:KPVIOB2S

pith:2014:KPVIOB2SNPVPXZ4EFKJPTFDUAB

not attested not anchored not stored refs pending

A description of the fundamental group in terms of commutators and closure operators

Marino Gran, Mathieu Duckerts-Antoine, Tomas Everaert

arxiv:1410.3218 v1 · 2014-10-13 · 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{KPVIOB2SNPVPXZ4EFKJPTFDUAB}

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	2026-05-18T02:40:11.813181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53ea8707526beafbe7842a92f99474007da816f5d7bd0ea314cc8a8efe44392c

Aliases

arxiv: 1410.3218 · arxiv_version: 1410.3218v1 · doi: 10.48550/arxiv.1410.3218 · pith_short_12: KPVIOB2SNPVP · pith_short_16: KPVIOB2SNPVPXZ4E · pith_short_8: KPVIOB2S

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/KPVIOB2SNPVPXZ4EFKJPTFDUAB \
  | 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: 53ea8707526beafbe7842a92f99474007da816f5d7bd0ea314cc8a8efe44392c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd62e5fc08e7e4bcdf8f9fa9eabf60852f859b1468b1a883409dc1c07f36fc46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2014-10-13T08:29:12Z",
    "title_canon_sha256": "9ac8959f08b179a0bf878f7b215a3c810886446a51b834b6971a6de266c4c161"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.3218",
    "kind": "arxiv",
    "version": 1
  }
}