Pith Number

pith:IV5M2GKM

pith:2016:IV5M2GKMMAARIBYW26IWSYJVEE

not attested not anchored not stored refs pending

Growth series for expansion complexes

James W. Cannon, Walter R. Parry, William J. Floyd

arxiv:1612.04771 v1 · 2016-12-14 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IV5M2GKMMAARIBYW26IWSYJVEE}

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	2026-05-18T00:54:58.654915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

457acd194c6001140716d7916961352139b153308255925d7a866899446247bb

Aliases

arxiv: 1612.04771 · arxiv_version: 1612.04771v1 · doi: 10.48550/arxiv.1612.04771 · pith_short_12: IV5M2GKMMAAR · pith_short_16: IV5M2GKMMAARIBYW · pith_short_8: IV5M2GKM

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/IV5M2GKMMAARIBYW26IWSYJVEE \
  | 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: 457acd194c6001140716d7916961352139b153308255925d7a866899446247bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "679a7ec93cefe3b48d1d9a372a5c64eb7fbaa0d6a6761886970843917ce3a054",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-12-14T18:54:36Z",
    "title_canon_sha256": "788cb3817cc0046afc35b7f8c3721ebc8178c95641beb77ab0b682ab7cdf142e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04771",
    "kind": "arxiv",
    "version": 1
  }
}