Pith Number

pith:OAEOL65L

pith:2012:OAEOL65LMV55BCO55WTLMFRJXM

not attested not anchored not stored refs pending

On the radical of multigraded modules

Ryota Okazaki, Viviana Ene

arxiv:1210.2026 v1 · 2012-10-07 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OAEOL65LMV55BCO55WTLMFRJXM}

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	2026-05-18T03:43:51.327874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7008e5fbab657bd089ddeda6b61629bb3bece5dabe7405671be06f7a682522b8

Aliases

arxiv: 1210.2026 · arxiv_version: 1210.2026v1 · doi: 10.48550/arxiv.1210.2026 · pith_short_12: OAEOL65LMV55 · pith_short_16: OAEOL65LMV55BCO5 · pith_short_8: OAEOL65L

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/OAEOL65LMV55BCO55WTLMFRJXM \
  | 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: 7008e5fbab657bd089ddeda6b61629bb3bece5dabe7405671be06f7a682522b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4db4ac91ba9d5d62aa24cf358d315d3629382d51414365d856ea8bd23750bf5c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-10-07T06:20:16Z",
    "title_canon_sha256": "1c9cbf036196b7037964fbbdc3dc6ba473111cee3b1d814c1a8f7c9bdc7cda50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2026",
    "kind": "arxiv",
    "version": 1
  }
}