Pith Number

pith:UNG5NPJV

pith:2016:UNG5NPJV2YBBF5XPBUYEKYWDGH

not attested not anchored not stored refs pending

On the cycle structure of the product of random maximal cycles

Boris Pittel, Miklos Bona

arxiv:1601.00319 v6 · 2016-01-03 · 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{UNG5NPJV2YBBF5XPBUYEKYWDGH}

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	2026-05-18T01:02:30.900578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a34dd6bd35d60212f6ef0d304562c331fa2544d1037fd7dd78eef6f8aa2294db

Aliases

arxiv: 1601.00319 · arxiv_version: 1601.00319v6 · doi: 10.48550/arxiv.1601.00319 · pith_short_12: UNG5NPJV2YBB · pith_short_16: UNG5NPJV2YBBF5XP · pith_short_8: UNG5NPJV

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/UNG5NPJV2YBBF5XPBUYEKYWDGH \
  | 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: a34dd6bd35d60212f6ef0d304562c331fa2544d1037fd7dd78eef6f8aa2294db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5507fcda33604f378315cb68d64432c3868e2449f596267d610aed6d28612b86",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-03T18:19:53Z",
    "title_canon_sha256": "5025b0097db34ca3f89db6166ff2079b4a7cfcfb243be31ccd63d66a1b15c768"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.00319",
    "kind": "arxiv",
    "version": 6
  }
}