Pith Number

pith:XPMRRAI6

pith:2010:XPMRRAI63CACQ7UHZPDA34RVUT

not attested not anchored not stored refs pending

The translation operator for self-projective coalgebras

William Chin

arxiv:1012.0318 v1 · 2010-12-01 · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPMRRAI63CACQ7UHZPDA34RVUT}

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	2026-05-18T04:34:17.992475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbd918811ed880287e87cbc60df235a4eb1b3f46eff13ec2fec380f636650d15

Aliases

arxiv: 1012.0318 · arxiv_version: 1012.0318v1 · doi: 10.48550/arxiv.1012.0318 · pith_short_12: XPMRRAI63CAC · pith_short_16: XPMRRAI63CACQ7UH · pith_short_8: XPMRRAI6

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/XPMRRAI63CACQ7UHZPDA34RVUT \
  | 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: bbd918811ed880287e87cbc60df235a4eb1b3f46eff13ec2fec380f636650d15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4a0eba25c5162d22bfb9d22417ab550025e8e4621c9aff7953d6ffb2a8f16dc",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-12-01T21:03:31Z",
    "title_canon_sha256": "d6ba79c11dd0f344b998757b392b1fd3adde583b578e11ff32d90133553007ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0318",
    "kind": "arxiv",
    "version": 1
  }
}