Pith Number

pith:HIFFCCJX

pith:2010:HIFFCCJXSQXFKUHFOKJM4CCUOY

not attested not anchored not stored refs pending

Singularities of the wave trace near cluster points of the length spectrum

David Jerison, Victor Guillemin, Yves Colin de Verdi\`ere

arxiv:1101.0099 v1 · 2010-12-30 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HIFFCCJXSQXFKUHFOKJM4CCUOY}

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	2026-05-18T04:32:11.044964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a0a510937942e5550e57292ce0854762ed4472b3882741f9faa599c5e9f3938

Aliases

arxiv: 1101.0099 · arxiv_version: 1101.0099v1 · doi: 10.48550/arxiv.1101.0099 · pith_short_12: HIFFCCJXSQXF · pith_short_16: HIFFCCJXSQXFKUHF · pith_short_8: HIFFCCJX

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/HIFFCCJXSQXFKUHFOKJM4CCUOY \
  | 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: 3a0a510937942e5550e57292ce0854762ed4472b3882741f9faa599c5e9f3938

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98379897b48645a717d3c65f918446348532de95c259f69889abbc7728623382",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-30T15:49:41Z",
    "title_canon_sha256": "4806d6540233e367bb9bfb2b47331d3490f9f655793906a93e75e61fa6142991"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0099",
    "kind": "arxiv",
    "version": 1
  }
}