Pith Number

pith:644CMMO3

pith:2015:644CMMO3OPIGFZXVROEUOJNX3N

not attested not anchored not stored refs pending

An isomorphism lemma for graded rings

James J. Zhang, Jason Bell

arxiv:1509.08812 v1 · 2015-09-29 · 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{644CMMO3OPIGFZXVROEUOJNX3N}

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	2026-05-18T01:31:47.041245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7382631db73d062e6f58b894725b7db68143dc2bc56b586f1cccd3ea56494b7

Aliases

arxiv: 1509.08812 · arxiv_version: 1509.08812v1 · doi: 10.48550/arxiv.1509.08812 · pith_short_12: 644CMMO3OPIG · pith_short_16: 644CMMO3OPIGFZXV · pith_short_8: 644CMMO3

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/644CMMO3OPIGFZXVROEUOJNX3N \
  | 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: f7382631db73d062e6f58b894725b7db68143dc2bc56b586f1cccd3ea56494b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9cce20468d24bef488d9dac2190d59bcb453a7c335bc71d5cbd495feae40d94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-09-29T15:42:02Z",
    "title_canon_sha256": "023c35308488fdab925e64991b0a28c177b50aa6fc8b170bacf1737742b91eba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08812",
    "kind": "arxiv",
    "version": 1
  }
}