Pith Number

pith:FQO5MTYT

pith:2016:FQO5MTYT6AHF22ON575JB27Y3Q

not attested not anchored not stored refs pending

Finite F-type and F-abundant modules

Hailong Dao, Tony Se

arxiv:1603.00334 v1 · 2016-03-01 · 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{FQO5MTYT6AHF22ON575JB27Y3Q}

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	2026-05-18T01:19:45.326757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c1dd64f13f00e5d69cdeffa90ebf8dc19c2070fe03666af2eda7a457ed63046

Aliases

arxiv: 1603.00334 · arxiv_version: 1603.00334v1 · doi: 10.48550/arxiv.1603.00334 · pith_short_12: FQO5MTYT6AHF · pith_short_16: FQO5MTYT6AHF22ON · pith_short_8: FQO5MTYT

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/FQO5MTYT6AHF22ON575JB27Y3Q \
  | 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: 2c1dd64f13f00e5d69cdeffa90ebf8dc19c2070fe03666af2eda7a457ed63046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f70ecee0ba0a22c2ae8215cea678cbeb59dabffbe8db5d917f4667d19e9c1775",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-03-01T16:02:31Z",
    "title_canon_sha256": "952bb7c1d9bfa53535958b50a8e4540d56d3241367825f8752fb6924c757a2d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00334",
    "kind": "arxiv",
    "version": 1
  }
}