Pith Number

pith:KMX2VR5T

pith:2004:KMX2VR5TO5RCKYRUUL46D6KWXW

not attested not anchored not stored refs pending

An Almost Sure Invariance Principle for Additive Functionals of Markov Chains

F. Rassoul-Agha, T. Seppalainen

arxiv:math/0411603 v2 · 2004-11-26 · 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{KMX2VR5TO5RCKYRUUL46D6KWXW}

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	2026-05-18T04:10:37.477007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

532faac7b37762256234a2f9e1f956bd9bedcf2e852f901ea9268ca729c42d6d

Aliases

arxiv: math/0411603 · arxiv_version: math/0411603v2 · doi: 10.48550/arxiv.math/0411603 · pith_short_12: KMX2VR5TO5RC · pith_short_16: KMX2VR5TO5RCKYRU · pith_short_8: KMX2VR5T

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/KMX2VR5TO5RCKYRUUL46D6KWXW \
  | 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: 532faac7b37762256234a2f9e1f956bd9bedcf2e852f901ea9268ca729c42d6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62ff5b806ecc43a42da1aa82d416da9277d17da97f685ce7c64e45f5813d0799",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-11-26T18:30:53Z",
    "title_canon_sha256": "8fac8c7d3c62d59284e5639198dfda4c88de1874bd09f448bc6a02eca76b587d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411603",
    "kind": "arxiv",
    "version": 2
  }
}