Pith Number

pith:S4TLP5HR

pith:2014:S4TLP5HRIBGHDIVTLNGGD5RQ2Y

not attested not anchored not stored refs pending

Almost-Ramanujan Graphs and Prime Gaps

Adrian Dudek

arxiv:1402.0620 v1 · 2014-02-04 · 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{S4TLP5HRIBGHDIVTLNGGD5RQ2Y}

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	2026-05-18T03:00:13.515130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9726b7f4f1404c71a2b35b4c61f630d638f549fea65ba19ebcd65635500b5657

Aliases

arxiv: 1402.0620 · arxiv_version: 1402.0620v1 · doi: 10.48550/arxiv.1402.0620 · pith_short_12: S4TLP5HRIBGH · pith_short_16: S4TLP5HRIBGHDIVT · pith_short_8: S4TLP5HR

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/S4TLP5HRIBGHDIVTLNGGD5RQ2Y \
  | 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: 9726b7f4f1404c71a2b35b4c61f630d638f549fea65ba19ebcd65635500b5657

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06b083c46b1e21bd438f40a54d61d3a06ea1c7034362b6a5d94bc998a57e66f3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-02-04T05:37:01Z",
    "title_canon_sha256": "4f8a3bb686a5d75090ba0798015ba19452878094067821663ffdf445cc2ce2da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.0620",
    "kind": "arxiv",
    "version": 1
  }
}