Pith Number

pith:7E5NT7NM

pith:2011:7E5NT7NMN4IPA6GT2Z2YW2C26Z

not attested not anchored not stored refs pending

Sharp Threshold Asymptotics for the Emergence of Additive Bases

Anant Godbole, Chang Mou Lim, Nicholas Triantafillou, Vince Lyzinski

arxiv:1110.1745 v3 · 2011-10-08 · math.CO · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7E5NT7NMN4IPA6GT2Z2YW2C26Z}

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	2026-05-18T03:58:13.975617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f93ad9fdac6f10f078d3d6758b685af64b499075937ccf9144ebd46ce7d36990

Aliases

arxiv: 1110.1745 · arxiv_version: 1110.1745v3 · doi: 10.48550/arxiv.1110.1745 · pith_short_12: 7E5NT7NMN4IP · pith_short_16: 7E5NT7NMN4IPA6GT · pith_short_8: 7E5NT7NM

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/7E5NT7NMN4IPA6GT2Z2YW2C26Z \
  | 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: f93ad9fdac6f10f078d3d6758b685af64b499075937ccf9144ebd46ce7d36990

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86cdc8295d7a626f2a4ec4644bbc4e8f385188be7e95acee878640d079abb21d",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-08T15:50:29Z",
    "title_canon_sha256": "2460c462d44be923aefbef8279f83f565dd8867971f219e1e0384c462b1a6386"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1745",
    "kind": "arxiv",
    "version": 3
  }
}