Pith Number

pith:ZR45A4HL

pith:2015:ZR45A4HLT2KU4OXHQ27S6E7LIN

not attested not anchored not stored refs pending

Ladder epochs and ladder chain of a Markov random walk with discrete driving chain

Gerold Alsmeyer

arxiv:1511.05361 v1 · 2015-11-17 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZR45A4HLT2KU4OXHQ27S6E7LIN}

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	2026-05-18T01:26:40.518147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc79d070eb9e954e3ae786bf2f13eb437d3302659101cd2d5a9c8f677704c801

Aliases

arxiv: 1511.05361 · arxiv_version: 1511.05361v1 · doi: 10.48550/arxiv.1511.05361 · pith_short_12: ZR45A4HLT2KU · pith_short_16: ZR45A4HLT2KU4OXH · pith_short_8: ZR45A4HL

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/ZR45A4HLT2KU4OXHQ27S6E7LIN \
  | 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: cc79d070eb9e954e3ae786bf2f13eb437d3302659101cd2d5a9c8f677704c801

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98cc5c786fcfba0497a2c84bb63690a3e5278692ca0b2c4649ebffc144ba3fcc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-17T11:56:14Z",
    "title_canon_sha256": "e11f6077f4974f5c048f99657504c6eabd926eb83829997c983c7496567153c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05361",
    "kind": "arxiv",
    "version": 1
  }
}