Pith Number

pith:PZAMUU3Y

pith:2026:PZAMUU3YDMRRLUGAUCLEOS4FFC

not attested not anchored not stored refs pending

Localized Centered Second-Chaos Operator

Guangqian Zhao

arxiv:2606.26065 v1 · 2026-06-24 · 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{PZAMUU3YDMRRLUGAUCLEOS4FFC}

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	2026-06-25T01:18:47.536601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e40ca53781b2315d0c0a096474b8528a5ebd174d431045e28be18f5e01887bc

Aliases

arxiv: 2606.26065 · arxiv_version: 2606.26065v1 · doi: 10.48550/arxiv.2606.26065 · pith_short_12: PZAMUU3YDMRR · pith_short_16: PZAMUU3YDMRRLUGA · pith_short_8: PZAMUU3Y

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/PZAMUU3YDMRRLUGAUCLEOS4FFC \
  | 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: 7e40ca53781b2315d0c0a096474b8528a5ebd174d431045e28be18f5e01887bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7eefb460f8af9192f5bd11dc336b7dc3f5c78c990094abd23b58abdce5306748",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-24T17:42:51Z",
    "title_canon_sha256": "ab77b1baa966f95edf1354ac70103c13db19c0a8f49617f646440c06eb235f2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26065",
    "kind": "arxiv",
    "version": 1
  }
}