Pith Number

pith:P7RRIE4J

pith:2016:P7RRIE4JZLWAE5UQWLQLIWF3OC

not attested not anchored not stored refs pending

The Hilbert function of bigraded algebras in $k[\mathbb{P}^1\times\mathbb{P}^1]$

Giuseppe Favacchio

arxiv:1609.06950 v3 · 2016-09-22 · 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{P7RRIE4JZLWAE5UQWLQLIWF3OC}

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	2026-05-18T00:40:01.355375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fe3141389caec027690b2e0b458bb709fe7c74d5ca05c550a7ee3420112e87a

Aliases

arxiv: 1609.06950 · arxiv_version: 1609.06950v3 · doi: 10.48550/arxiv.1609.06950 · pith_short_12: P7RRIE4JZLWA · pith_short_16: P7RRIE4JZLWAE5UQ · pith_short_8: P7RRIE4J

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/P7RRIE4JZLWAE5UQWLQLIWF3OC \
  | 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: 7fe3141389caec027690b2e0b458bb709fe7c74d5ca05c550a7ee3420112e87a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42d5c95432df85cd5f32cab04a950515e36decaff9ab9daf0ffb1e059ac2870a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-09-22T12:57:33Z",
    "title_canon_sha256": "7e7f9d1df06bf39e7cac30bbe66a88ba67f0ffa4c3e3c5806c70a7419818bee1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06950",
    "kind": "arxiv",
    "version": 3
  }
}