Pith Number

pith:OEAPUAAH

pith:2025:OEAPUAAHJDZ5LN5BWCWNJPE4YD

not attested not anchored not stored refs pending

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus

Hui Zhu, Massimo Sorella, Nicolas Burq, Pierre Germain

arxiv:2507.16599 v1 · 2025-07-22 · math.AP · math-ph · math.CA · math.MP · math.NT · 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{OEAPUAAHJDZ5LN5BWCWNJPE4YD}

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	2026-07-05T11:41:27.526369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7100fa000748f3d5b7a1b0acd4bc9cc0f30dca7c6217fcab48839a404d11d12c

Aliases

arxiv: 2507.16599 · arxiv_version: 2507.16599v1 · doi: 10.48550/arxiv.2507.16599 · pith_short_12: OEAPUAAHJDZ5 · pith_short_16: OEAPUAAHJDZ5LN5B · pith_short_8: OEAPUAAH

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/OEAPUAAHJDZ5LN5BWCWNJPE4YD \
  | 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: 7100fa000748f3d5b7a1b0acd4bc9cc0f30dca7c6217fcab48839a404d11d12c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46c86418c87176d3b8efa68d3a6a235669b7b15e2a4ad7bb3b693c88dee04b77",
    "cross_cats_sorted": [
      "math-ph",
      "math.CA",
      "math.MP",
      "math.NT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-22T13:56:40Z",
    "title_canon_sha256": "c0ab2440ac429e38e1d4b6a7356784f22152eaa0dcc62090a211605bd26bbb92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16599",
    "kind": "arxiv",
    "version": 1
  }
}