Pith Number

pith:FNFN5525

pith:2026:FNFN55253BUMJ6G3B7VYS6XN3N

not attested not anchored not stored refs pending

Orthonormal Spectral Cluster Bounds on Manifolds with Nonpositive Curvature

Jean-Claude Cuenin, Ngoc Nhi Nguyen, Xiaoyan Su

arxiv:2606.12964 v1 · 2026-06-11 · math.AP · 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{FNFN55253BUMJ6G3B7VYS6XN3N}

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	2026-06-12T01:09:35.642886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b4adef75dd868c4f8db0feb897aeddb51a4a98fc758aeed8afbcfb870e33bc2

Aliases

arxiv: 2606.12964 · arxiv_version: 2606.12964v1 · doi: 10.48550/arxiv.2606.12964 · pith_short_12: FNFN55253BUM · pith_short_16: FNFN55253BUMJ6G3 · pith_short_8: FNFN5525

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/FNFN55253BUMJ6G3B7VYS6XN3N \
  | 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: 2b4adef75dd868c4f8db0feb897aeddb51a4a98fc758aeed8afbcfb870e33bc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44a05ed6f04d4a3d6f7a3d6e19cd901e2f3c68491d4edd23040cafaf8d20c608",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-11T06:49:26Z",
    "title_canon_sha256": "a444bb8120af2629494753da926c94fe320c545f616bcc75986e56178af39931"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12964",
    "kind": "arxiv",
    "version": 1
  }
}