Pith Number

pith:6VYPNYVJ

pith:2015:6VYPNYVJFKW77EEZHQ3FQHS6KC

not attested not anchored not stored refs pending

Size biased couplings and the spectral gap for random regular graphs

Larry Goldstein, Nicholas A. Cook, Tobias Johnson

arxiv:1510.06013 v3 · 2015-10-20 · 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{6VYPNYVJFKW77EEZHQ3FQHS6KC}

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	2026-05-18T00:24:10.587950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f570f6e2a92aadff90993c36581e5e50bf26957b47e245205cc2de960ee4b1fb

Aliases

arxiv: 1510.06013 · arxiv_version: 1510.06013v3 · doi: 10.48550/arxiv.1510.06013 · pith_short_12: 6VYPNYVJFKW7 · pith_short_16: 6VYPNYVJFKW77EEZ · pith_short_8: 6VYPNYVJ

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/6VYPNYVJFKW77EEZHQ3FQHS6KC \
  | 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: f570f6e2a92aadff90993c36581e5e50bf26957b47e245205cc2de960ee4b1fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47b2cbbcf8190b37b0aec83e61e5e0ccb5626af0259e6287692971bbe01498c0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-20T19:16:46Z",
    "title_canon_sha256": "7c2ba00b7dd657185c49eb7b758cbae54d2dbe46ec14527e1ffc366e5807bf51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06013",
    "kind": "arxiv",
    "version": 3
  }
}