Pith Number

pith:XP52JE77

pith:2013:XP52JE77P3KPKKLV4COWMSA2MT

not attested not anchored not stored refs pending

Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

Xiangui Zhao, Yang Zhang

arxiv:1312.2044 v2 · 2013-12-07 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XP52JE77P3KPKKLV4COWMSA2MT}

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	2026-05-18T03:03:22.598333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbfba493ff7ed4f52975e09d66481a64c7cc23d75fda62b11bb195220783b1ad

Aliases

arxiv: 1312.2044 · arxiv_version: 1312.2044v2 · doi: 10.48550/arxiv.1312.2044 · pith_short_12: XP52JE77P3KP · pith_short_16: XP52JE77P3KPKKLV · pith_short_8: XP52JE77

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/XP52JE77P3KPKKLV4COWMSA2MT \
  | 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: bbfba493ff7ed4f52975e09d66481a64c7cc23d75fda62b11bb195220783b1ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e17b6966eabc6966238cbbd58996857e85077f01c5e643379a1bced28903ef7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-12-07T00:38:34Z",
    "title_canon_sha256": "7a2914ad603395931f479aee3645b686f30dfe9f284686522fa4c06033acad13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2044",
    "kind": "arxiv",
    "version": 2
  }
}