Pith Number

pith:MCK4S3GE

pith:2003:MCK4S3GEI6MPNGKG4QF62PFIJ4

not attested not anchored not stored refs pending

Eigenfrequencies and expansions for damped wave equations

Michael Hitrik

arxiv:math/0309250 v1 · 2003-09-15 · math.SP · 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{MCK4S3GEI6MPNGKG4QF62PFIJ4}

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	2026-07-04T14:37:43.417160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6095c96cc44798f69946e40bed3ca84f0b7a12522a091ac1bae298b2421a8d81

Aliases

arxiv: math/0309250 · arxiv_version: math/0309250v1 · doi: 10.48550/arxiv.math/0309250 · pith_short_12: MCK4S3GEI6MP · pith_short_16: MCK4S3GEI6MPNGKG · pith_short_8: MCK4S3GE

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/MCK4S3GEI6MPNGKG4QF62PFIJ4 \
  | 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: 6095c96cc44798f69946e40bed3ca84f0b7a12522a091ac1bae298b2421a8d81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e61da10b5d62cb8c5b12c288b95526ba5f282c2fb6d23de43f685cb70c6c79d9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2003-09-15T20:55:37Z",
    "title_canon_sha256": "7ec24624fb84634ccb9a5744ca03d39890ae878199ec51ca673c2a2b284661cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309250",
    "kind": "arxiv",
    "version": 1
  }
}