Pith Number

pith:I4CULLDR

pith:2013:I4CULLDREJOIQNDK26HOHXFJ3Q

not attested not anchored not stored refs pending

Digraphs and cycle polynomials for free-by-cyclic groups

Eriko Hironaka, Kasra Rafi, Yael Algom-Kfir

arxiv:1310.7533 v2 · 2013-10-28 · 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{I4CULLDREJOIQNDK26HOHXFJ3Q}

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	2026-05-18T02:57:26.348852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

470545ac71225c88346ad78ee3dca9dc01adc01edbb55e0f403a6a2f923824a8

Aliases

arxiv: 1310.7533 · arxiv_version: 1310.7533v2 · doi: 10.48550/arxiv.1310.7533 · pith_short_12: I4CULLDREJOI · pith_short_16: I4CULLDREJOIQNDK · pith_short_8: I4CULLDR

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/I4CULLDREJOIQNDK26HOHXFJ3Q \
  | 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: 470545ac71225c88346ad78ee3dca9dc01adc01edbb55e0f403a6a2f923824a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94cb39611bb10d1e80eee2181a5ea7808282ec1b3b850d6849f42052fbf4cd17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-10-28T18:57:56Z",
    "title_canon_sha256": "9b45edc4914d46c777c4e22969560f1b0c35e014c98424816d3107ab5c163b2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7533",
    "kind": "arxiv",
    "version": 2
  }
}