Pith Number

pith:Z4MY32CT

pith:2011:Z4MY32CTVWDEWP7DSCM7HOOAM4

not attested not anchored not stored refs pending

Sylvester's double sums: an inductive proof of the general case

Agnes Szanto, Teresa Krick

arxiv:1106.4770 v1 · 2011-06-23 · math.AC · 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{Z4MY32CTVWDEWP7DSCM7HOOAM4}

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	2026-05-18T04:19:23.700951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf198de853ad864b3fe39099f3b9c067280c8bd00fb595f6626ed934fd547f88

Aliases

arxiv: 1106.4770 · arxiv_version: 1106.4770v1 · doi: 10.48550/arxiv.1106.4770 · pith_short_12: Z4MY32CTVWDE · pith_short_16: Z4MY32CTVWDEWP7D · pith_short_8: Z4MY32CT

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/Z4MY32CTVWDEWP7DSCM7HOOAM4 \
  | 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: cf198de853ad864b3fe39099f3b9c067280c8bd00fb595f6626ed934fd547f88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14697774acf088ffb7c608b4d0d25ddb9405578517263955f2dcf8f163777c16",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-06-23T16:41:17Z",
    "title_canon_sha256": "820816a28b68bf8a382839e6e4a63c8fc632dbe37970e26d54f3b5d0797af815"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4770",
    "kind": "arxiv",
    "version": 1
  }
}