Pith Number

pith:QG7Q3RFR

pith:2026:QG7Q3RFREYIZ6IMEOTG4UE5QEI

not attested not anchored not stored refs pending

Laskar's frequency map analysis revisited

Yong Li, Zhicheng Tong

arxiv:2608.02182 v1 · 2026-08-03 · math.DS · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QG7Q3RFREYIZ6IMEOTG4UE5QEI}

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	2026-08-04T02:11:20.954015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81bf0dc4b126119f218474cdca13b0222b4e92033b9856b40a7f31399dbbda46

Aliases

arxiv: 2608.02182 · arxiv_version: 2608.02182v1 · doi: 10.48550/arxiv.2608.02182 · pith_short_12: QG7Q3RFREYIZ · pith_short_16: QG7Q3RFREYIZ6IME · pith_short_8: QG7Q3RFR

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/QG7Q3RFREYIZ6IMEOTG4UE5QEI \
  | 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: 81bf0dc4b126119f218474cdca13b0222b4e92033b9856b40a7f31399dbbda46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a37098fa2f456afd9520f6451e72008c2784405e3779d7dcb98fe5bd179460a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-08-03T13:05:58Z",
    "title_canon_sha256": "d88d5952e26c78e75338d0a7cf26c08c7ef90646d6d9e04c98918f8b7abe05fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.02182",
    "kind": "arxiv",
    "version": 1
  }
}