Pith Number

pith:U7L3MPBF

pith:2010:U7L3MPBFP7TJAUNTBLOQM3SBO3

not attested not anchored not stored refs pending

Alexander duality and Stanley depth of multigraded modules

Kohji Yanagawa, Ryota Okazaki

arxiv:1003.4008 v3 · 2010-03-21 · 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{U7L3MPBFP7TJAUNTBLOQM3SBO3}

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	2026-05-18T04:30:14.482698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7d7b63c257fe69051b30add066e4176d353ddff4e48f6e5f8e6c91dde57232a

Aliases

arxiv: 1003.4008 · arxiv_version: 1003.4008v3 · doi: 10.48550/arxiv.1003.4008 · pith_short_12: U7L3MPBFP7TJ · pith_short_16: U7L3MPBFP7TJAUNT · pith_short_8: U7L3MPBF

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/U7L3MPBFP7TJAUNTBLOQM3SBO3 \
  | 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: a7d7b63c257fe69051b30add066e4176d353ddff4e48f6e5f8e6c91dde57232a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccb59c58335621ffbdc216edce24f74822c5fde21679feef624659ecf78e79ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-03-21T16:54:37Z",
    "title_canon_sha256": "efe1ee05fbc0481303caefe312cb007bb8e2d8c9cb1fbbdb62549e59f77f052a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.4008",
    "kind": "arxiv",
    "version": 3
  }
}