Pith Number

pith:OTK2Z2QV

pith:2015:OTK2Z2QVG4GYHQZAM5LVZB7ZWV

not attested not anchored not stored refs pending

Gaps Between Almost-Primes and a Construction of Almost-Ramanujan Graphs

Adrian Dudek

arxiv:1502.01693 v1 · 2015-01-29 · 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{OTK2Z2QVG4GYHQZAM5LVZB7ZWV}

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	2026-05-18T02:27:51.513514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74d5acea15370d83c32067575c87f9b546f985735b54ffa3f0e53fe93c0c7eb3

Aliases

arxiv: 1502.01693 · arxiv_version: 1502.01693v1 · doi: 10.48550/arxiv.1502.01693 · pith_short_12: OTK2Z2QVG4GY · pith_short_16: OTK2Z2QVG4GYHQZA · pith_short_8: OTK2Z2QV

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/OTK2Z2QVG4GYHQZAM5LVZB7ZWV \
  | 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: 74d5acea15370d83c32067575c87f9b546f985735b54ffa3f0e53fe93c0c7eb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4c9b81bf9091a3e250542815595c230d5e3b5d97a8e9be4bb3c632615f9b84a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-29T23:43:17Z",
    "title_canon_sha256": "cb86274e54a6edc755e998e08df7c43112e9dcd57d9791b34018cf9243079dc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01693",
    "kind": "arxiv",
    "version": 1
  }
}