Pith Number

pith:DV56HILP

pith:2007:DV56HILPEZH5WQY7GXPXDMSKGF

not attested not anchored not stored refs pending

A Birthday Paradox for Markov chains with an optimal bound for collision in the Pollard Rho algorithm for discrete logarithm

Jeong Han Kim, Prasad Tetali, Ravi Montenegro, Yuval Peres

arxiv:0712.0220 v2 · 2007-12-03 · 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{DV56HILPEZH5WQY7GXPXDMSKGF}

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	2026-05-18T01:05:13.912370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d7be3a16f264fdb431f35df71b24a316859d96fb3673a9ab27099ff5e230961

Aliases

arxiv: 0712.0220 · arxiv_version: 0712.0220v2 · doi: 10.48550/arxiv.0712.0220 · pith_short_12: DV56HILPEZH5 · pith_short_16: DV56HILPEZH5WQY7 · pith_short_8: DV56HILP

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/DV56HILPEZH5WQY7GXPXDMSKGF \
  | 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: 1d7be3a16f264fdb431f35df71b24a316859d96fb3673a9ab27099ff5e230961

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9648beebf7a37683fdc3e8e7c68053c65128ef23688c57d88cf91841916b6db3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-12-03T07:16:00Z",
    "title_canon_sha256": "05f0d8b03f2b22d0dba680fa8261eabfef7ca65e5822154a279d4262e750bb43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.0220",
    "kind": "arxiv",
    "version": 2
  }
}