Pith Number

pith:5GM5H3DZ

pith:2009:5GM5H3DZD7UAVTOFJZHGCRJONY

not attested not anchored not stored refs pending

A remainder estimate for Weyl's law on Liouville tori

Hugues Lapointe

arxiv:0903.2518 v3 · 2009-03-14 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5GM5H3DZD7UAVTOFJZHGCRJONY}

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	2026-07-04T17:27:53.124890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e999d3ec791fe80acdc54e4e61452e6e29e618fec8888bf7273f109707208733

Aliases

arxiv: 0903.2518 · arxiv_version: 0903.2518v3 · doi: 10.48550/arxiv.0903.2518 · pith_short_12: 5GM5H3DZD7UA · pith_short_16: 5GM5H3DZD7UAVTOF · pith_short_8: 5GM5H3DZ

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/5GM5H3DZD7UAVTOFJZHGCRJONY \
  | 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: e999d3ec791fe80acdc54e4e61452e6e29e618fec8888bf7273f109707208733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "717aa80a137f95f476dafe862cd566d713ba453e69739f7e6582e0b1a18ff668",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-03-14T00:31:05Z",
    "title_canon_sha256": "f66c1ca6120f921116f3f7fc30fe452f9dbe9a35c57eddf566d17d71faf9adb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2518",
    "kind": "arxiv",
    "version": 3
  }
}