Pith Number

pith:HRIFOLW3

pith:2026:HRIFOLW3OF447I63UZZHZNCW36

not attested not anchored not stored refs pending

Convergence Rate of Birkhoff Average for Toral Quasi-Periodic Rotations and Applications

Jianlu Zhang, Son N.T. Tu

arxiv:2608.02489 v1 · 2026-08-03 · math.AP · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRIFOLW3OF447I63UZZHZNCW36}

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	2026-08-04T02:43:47.086636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c50572edb7179cfa3dba6727cb456dfafcc99277e3d7eee2baba42bad7a005c

Aliases

arxiv: 2608.02489 · arxiv_version: 2608.02489v1 · doi: 10.48550/arxiv.2608.02489 · pith_short_12: HRIFOLW3OF44 · pith_short_16: HRIFOLW3OF447I63 · pith_short_8: HRIFOLW3

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/HRIFOLW3OF447I63UZZHZNCW36 \
  | 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: 3c50572edb7179cfa3dba6727cb456dfafcc99277e3d7eee2baba42bad7a005c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e0980572b751450c031bb591f81bf26b55541fd47629a8a8b95e295ea1a29fc",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-03T16:53:57Z",
    "title_canon_sha256": "0018120032b10193aab9a71d5f6be7fd8564697c2a8041f4d5ecbbc1c3450b83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.02489",
    "kind": "arxiv",
    "version": 1
  }
}