Pith Number

pith:VC4RXWZ6

pith:2009:VC4RXWZ6RS7FTKGATQVI4F7CTM

not attested not anchored not stored refs pending

Invariants of isospectral deformations and spectral rigidity

G. Popov, P. Topalov

arxiv:0906.0449 v3 · 2009-06-02 · 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{VC4RXWZ6RS7FTKGATQVI4F7CTM}

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	2026-05-18T04:33:18.189803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8b91bdb3e8cbe59a8c09c2a8e17e29b3f2551abc9e088cbc04a3793b8a5026e

Aliases

arxiv: 0906.0449 · arxiv_version: 0906.0449v3 · doi: 10.48550/arxiv.0906.0449 · pith_short_12: VC4RXWZ6RS7F · pith_short_16: VC4RXWZ6RS7FTKGA · pith_short_8: VC4RXWZ6

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/VC4RXWZ6RS7FTKGATQVI4F7CTM \
  | 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: a8b91bdb3e8cbe59a8c09c2a8e17e29b3f2551abc9e088cbc04a3793b8a5026e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "457507a3972d9c25fbb34a1c81d7d5e12e0e611b4db4a225b4bf08aee44b3719",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-06-02T09:27:39Z",
    "title_canon_sha256": "9995bc0de40fea2346a3f37ea8772cb41c9c4309e4112ba917966e67ef87b139"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.0449",
    "kind": "arxiv",
    "version": 3
  }
}