Pith Number

pith:3ZFX7P3Q

pith:2016:3ZFX7P3QLALUB6XKDSCOOYCRIQ

not attested not anchored not stored refs pending

The spectral gap of dense random regular graphs

Konstantin Tikhomirov, Pierre Youssef

arxiv:1610.01765 v2 · 2016-10-06 · math.PR · 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{3ZFX7P3QLALUB6XKDSCOOYCRIQ}

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	2026-05-17T23:57:00.917948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de4b7fbf70581740faea1c84e760514426eb35713f667a17ffa3b3c2ecee4363

Aliases

arxiv: 1610.01765 · arxiv_version: 1610.01765v2 · doi: 10.48550/arxiv.1610.01765 · pith_short_12: 3ZFX7P3QLALU · pith_short_16: 3ZFX7P3QLALUB6XK · pith_short_8: 3ZFX7P3Q

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/3ZFX7P3QLALUB6XKDSCOOYCRIQ \
  | 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: de4b7fbf70581740faea1c84e760514426eb35713f667a17ffa3b3c2ecee4363

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42d5c320c5fb6ae63106c8d8402864285865a8fbb69f98c3ba184c43946c5555",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-06T07:54:39Z",
    "title_canon_sha256": "adb2a8a591e0f338ea3bd86df993464b9992b38ee3e0b4139233cb785370e8ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01765",
    "kind": "arxiv",
    "version": 2
  }
}