Pith Number

pith:UPOB26OS

pith:2006:UPOB26OSKOS2GIMNK35ELGT7VV

not attested not anchored not stored refs pending

Mixing times via super-fast coupling

Robert Burton, Yevgeniy Kovchegov

arxiv:math/0609568 v3 · 2006-09-20 · 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{UPOB26OSKOS2GIMNK35ELGT7VV}

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	2026-05-18T04:12:56.626640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3dc1d79d253a5a3218d56fa459a7fad74b833cbc19940040f815bcb7e9e79c0

Aliases

arxiv: math/0609568 · arxiv_version: math/0609568v3 · doi: 10.48550/arxiv.math/0609568 · pith_short_12: UPOB26OSKOS2 · pith_short_16: UPOB26OSKOS2GIMN · pith_short_8: UPOB26OS

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/UPOB26OSKOS2GIMNK35ELGT7VV \
  | 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: a3dc1d79d253a5a3218d56fa459a7fad74b833cbc19940040f815bcb7e9e79c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "468ac2dc21b7f7fbecb4707a48ba6b7cb7c0761b19a36930582d964b8cd9eebc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2006-09-20T17:35:19Z",
    "title_canon_sha256": "a03de7c8e31e634fdc324b397e73ed76b53bf109f58816498c9ad6b0aac44ac5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609568",
    "kind": "arxiv",
    "version": 3
  }
}