Pith Number

pith:KNREF35F

pith:2012:KNREF35F7D2TEJEOVXVCLIPLDJ

not attested not anchored not stored refs pending

Robust Transitivity for Endomorphisms

Cristina Lizana, Enrique Pujals

arxiv:1201.4806 v2 · 2012-01-23 · 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{KNREF35F7D2TEJEOVXVCLIPLDJ}

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	2026-05-18T03:59:49.087822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

536242efa5f8f532248eadea25a1eb1a6357686885b6ca5e6793dad99e18baff

Aliases

arxiv: 1201.4806 · arxiv_version: 1201.4806v2 · doi: 10.48550/arxiv.1201.4806 · pith_short_12: KNREF35F7D2T · pith_short_16: KNREF35F7D2TEJEO · pith_short_8: KNREF35F

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/KNREF35F7D2TEJEOVXVCLIPLDJ \
  | 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: 536242efa5f8f532248eadea25a1eb1a6357686885b6ca5e6793dad99e18baff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04f5537e797225f5cf740b0ab7bd10f983de16be610a8203a9b4be5b079a5196",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-01-23T18:40:51Z",
    "title_canon_sha256": "795687b51a72aac766f6496e1d3ca49d2f64515fb2be2d5003ff360f1cf22ffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4806",
    "kind": "arxiv",
    "version": 2
  }
}