Pith Number

pith:7CAW3C7F

pith:2017:7CAW3C7FF2FVXO42TLKAXNZHYZ

not attested not anchored not stored refs pending

Conditional expanding bounds for two-variable functions over arbitrary fields

Hossein Nassajian Mojarrad, Thang Pham

arxiv:1703.03309 v2 · 2017-03-09 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7CAW3C7FF2FVXO42TLKAXNZHYZ}

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	2026-05-18T00:47:56.348769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8816d8be52e8b5bbb9a9ad40bb727c645d13913a89cf9554db8d2b43614e39b

Aliases

arxiv: 1703.03309 · arxiv_version: 1703.03309v2 · doi: 10.48550/arxiv.1703.03309 · pith_short_12: 7CAW3C7FF2FV · pith_short_16: 7CAW3C7FF2FVXO42 · pith_short_8: 7CAW3C7F

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/7CAW3C7FF2FVXO42TLKAXNZHYZ \
  | 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: f8816d8be52e8b5bbb9a9ad40bb727c645d13913a89cf9554db8d2b43614e39b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a25453516fe6ee95194b5d02d585f37dda52f1b7b49099bb39736c6564beb8c4",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-03-09T15:52:06Z",
    "title_canon_sha256": "6ce3a60332795d916c0938270334c79d48315ae88851f404059ea8201c269494"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.03309",
    "kind": "arxiv",
    "version": 2
  }
}