Pith Number

pith:CECMTQSX

pith:2009:CECMTQSXMVIIXKU3RCQBWWDDOD

not attested not anchored not stored refs pending

On the X-rank with respect to linear projections of projective varieties

Alessandra Bernardi, Edoardo Ballico

arxiv:0912.4834 v2 · 2009-12-24 · math.AG · 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{CECMTQSXMVIIXKU3RCQBWWDDOD}

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	2026-05-18T04:07:54.366006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1104c9c25765508baa9b88a01b586370fec55c77b68677f06367a0075cd1ba09

Aliases

arxiv: 0912.4834 · arxiv_version: 0912.4834v2 · doi: 10.48550/arxiv.0912.4834 · pith_short_12: CECMTQSXMVII · pith_short_16: CECMTQSXMVIIXKU3 · pith_short_8: CECMTQSX

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/CECMTQSXMVIIXKU3RCQBWWDDOD \
  | 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: 1104c9c25765508baa9b88a01b586370fec55c77b68677f06367a0075cd1ba09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c12032404db51b17b3abe92b98b39ec932e3ce0c898255ff787a61e83912b4ca",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-12-24T11:15:56Z",
    "title_canon_sha256": "49508f7c24896fc3fa17efb6305d9b6ec81c10c279b7eb606e7b13a142435458"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4834",
    "kind": "arxiv",
    "version": 2
  }
}