Pith Number

pith:M5MMT5GT

pith:2010:M5MMT5GT7GVABSDPWG7PQCRMYP

not attested not anchored not stored refs pending

Hilbert functions and set of points in $\mathbb P^1\times \mathbb P^1$

Lucia Marino, Paola Bonacini

arxiv:1009.4059 v2 · 2010-09-21 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M5MMT5GT7GVABSDPWG7PQCRMYP}

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	2026-05-18T04:14:05.927073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6758c9f4d3f9aa00c86fb1bef80a2cc3fcecea7e36baa82806d373295447c1b2

Aliases

arxiv: 1009.4059 · arxiv_version: 1009.4059v2 · doi: 10.48550/arxiv.1009.4059 · pith_short_12: M5MMT5GT7GVA · pith_short_16: M5MMT5GT7GVABSDP · pith_short_8: M5MMT5GT

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/M5MMT5GT7GVABSDPWG7PQCRMYP \
  | 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: 6758c9f4d3f9aa00c86fb1bef80a2cc3fcecea7e36baa82806d373295447c1b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6e84e820ff84ebf25b18a56e2baf2bfd2774b7312ccb0f263241bb4ef544af8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-09-21T11:12:02Z",
    "title_canon_sha256": "e3097f4b5f75bb5fbb56923c5e2a8ec7828cc505bae37b6e72ad40b1bb34f54a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4059",
    "kind": "arxiv",
    "version": 2
  }
}