Pith Number

pith:PHDFNP32

pith:2012:PHDFNP32KDFAH6PQI3PIJWEXVH

not attested not anchored not stored refs pending

Topological realizations and fundamental groups of higher-rank graphs

Aidan Sims, Alex Kumjian, John Quigg, S. Kaliszewski

arxiv:1205.2858 v1 · 2012-05-13 · math.CO · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHDFNP32KDFAH6PQI3PIJWEXVH}

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	2026-05-18T03:55:45.832397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79c656bf7a50ca03f9f046de84d897a9ec409408a4dd18c6ce8eda857ccfb881

Aliases

arxiv: 1205.2858 · arxiv_version: 1205.2858v1 · doi: 10.48550/arxiv.1205.2858 · pith_short_12: PHDFNP32KDFA · pith_short_16: PHDFNP32KDFAH6PQ · pith_short_8: PHDFNP32

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/PHDFNP32KDFAH6PQI3PIJWEXVH \
  | 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: 79c656bf7a50ca03f9f046de84d897a9ec409408a4dd18c6ce8eda857ccfb881

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "118bf4e7d6b2e314a5e4eb62e117ad5377e95973dc9cf710bc1a5176a8cd253e",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-13T13:34:06Z",
    "title_canon_sha256": "028ee5f95edd5adee54b7217ac88c32cf9b149d373a66c76bd1ada33fdf4fad8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2858",
    "kind": "arxiv",
    "version": 1
  }
}