Pith Number

pith:YTZ6H5IW

pith:2022:YTZ6H5IW73VMHHHT7ST2RTT2PV

not attested not anchored not stored refs pending

Ray-Knight compactification of birth and death processes

Liping Li

arxiv:2211.12369 v3 · 2022-11-22 · 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{YTZ6H5IW73VMHHHT7ST2RTT2PV}

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	2026-07-05T08:56:11.474948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4f3e3f516feeac39cf3fca7a8ce7a7d44fc32632cc238f26aad8fcd3af360c6

Aliases

arxiv: 2211.12369 · arxiv_version: 2211.12369v3 · doi: 10.48550/arxiv.2211.12369 · pith_short_12: YTZ6H5IW73VM · pith_short_16: YTZ6H5IW73VMHHHT · pith_short_8: YTZ6H5IW

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/YTZ6H5IW73VMHHHT7ST2RTT2PV \
  | 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: c4f3e3f516feeac39cf3fca7a8ce7a7d44fc32632cc238f26aad8fcd3af360c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb554a1e3f7385800756ce43cad457e256ca6a4de205cebe92646b318fbe37b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-11-22T16:04:23Z",
    "title_canon_sha256": "8b4b1b463dfa9f2ec91a6acf1c9bf43b6f7f80b20551f256233ad2ed828d1f0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.12369",
    "kind": "arxiv",
    "version": 3
  }
}