Pith Number

pith:5W7WRCNP

pith:2006:5W7WRCNP4UA24CXZMP2BC526MD

not attested not anchored not stored refs pending

A lower bound for |{a+b: a\in A, b\in B, P(a,b)\not=0}|

Hao Pan, Zhi-Wei Sun

arxiv:math/0610892 v1 · 2006-10-29 · math.NT · 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{5W7WRCNP4UA24CXZMP2BC526MD}

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	2026-07-04T14:57:11.344728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edbf6889afe501ae0af963f411775e60c5a6d136cffab4144c8068c0d9564790

Aliases

arxiv: math/0610892 · arxiv_version: math/0610892v1 · doi: 10.48550/arxiv.math/0610892 · pith_short_12: 5W7WRCNP4UA2 · pith_short_16: 5W7WRCNP4UA24CXZ · pith_short_8: 5W7WRCNP

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/5W7WRCNP4UA24CXZMP2BC526MD \
  | 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: edbf6889afe501ae0af963f411775e60c5a6d136cffab4144c8068c0d9564790

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22f02977a36e59c3713004e3e64164c500176d4de1c9ac50ada7a526d607dcdd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-10-29T13:44:39Z",
    "title_canon_sha256": "7702230341781de723f711554205883fb52d6f0e1b4fc402722722720449f496"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610892",
    "kind": "arxiv",
    "version": 1
  }
}