Pith Number

pith:UJTX3ZQ5

pith:2015:UJTX3ZQ5LLH65QCKWTIAJYAKWH

not attested not anchored not stored refs pending

Schwartz-Zippel bounds for two-dimensional products

Claudiu Valculescu, Frank de Zeeuw, Hossein Nassajian Mojarrad, Thang Pham

arxiv:1507.08181 v5 · 2015-07-29 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UJTX3ZQ5LLH65QCKWTIAJYAKWH}

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	2026-05-18T00:27:36.901794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2677de61d5acfeec04ab4d004e00ab1d4651b7cb2c87ca361eadadffc4fd55d

Aliases

arxiv: 1507.08181 · arxiv_version: 1507.08181v5 · doi: 10.48550/arxiv.1507.08181 · pith_short_12: UJTX3ZQ5LLH6 · pith_short_16: UJTX3ZQ5LLH65QCK · pith_short_8: UJTX3ZQ5

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/UJTX3ZQ5LLH65QCKWTIAJYAKWH \
  | 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: a2677de61d5acfeec04ab4d004e00ab1d4651b7cb2c87ca361eadadffc4fd55d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b2aed67d05ec0c1f41c21448ef64d2f5e1f1119925331701d7e6b3b31beb4f7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-29T15:19:16Z",
    "title_canon_sha256": "d06fed68157bfabffc6865aeda2ba94ce608e69b453f1b3f81b5da88e913800c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08181",
    "kind": "arxiv",
    "version": 5
  }
}