Pith Number

pith:QVFIPZCN

pith:2013:QVFIPZCNKL6NTI43WS7WB4RVZP

not attested not anchored not stored refs pending

Combinatorial Nullstellensatz Approach to Polynomial Expanding

Fedor Petrov

arxiv:1309.3935 v1 · 2013-09-16 · math.CO · 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{QVFIPZCNKL6NTI43WS7WB4RVZP}

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	2026-05-18T03:13:11.794375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

854a87e44d52fcd9a39bb4bf60f235cbc17ca20314dbb7e1516a9f77417997cb

Aliases

arxiv: 1309.3935 · arxiv_version: 1309.3935v1 · doi: 10.48550/arxiv.1309.3935 · pith_short_12: QVFIPZCNKL6N · pith_short_16: QVFIPZCNKL6NTI43 · pith_short_8: QVFIPZCN

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/QVFIPZCNKL6NTI43WS7WB4RVZP \
  | 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: 854a87e44d52fcd9a39bb4bf60f235cbc17ca20314dbb7e1516a9f77417997cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdc4d31a60c46ad3c45cec59d366eaf6d7476de2d6d92ce16cf3929d1c25876b",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-16T12:48:30Z",
    "title_canon_sha256": "127cbbf22806006c0ec43933a8c6b56f99d81fcd39ab8c8309c3bd27581a6de1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3935",
    "kind": "arxiv",
    "version": 1
  }
}