Pith Number

pith:HK5BHQ3F

pith:2016:HK5BHQ3FPHWDK7H57ZMSS2QSYH

not attested not anchored not stored refs pending

From K.A.M. Tori to Isospectral Invariants and Spectral Rigidity of Billiard Tables

G. Popov, P. Topalov

arxiv:1602.03155 v2 · 2016-02-09 · math.SP · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HK5BHQ3FPHWDK7H57ZMSS2QSYH}

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	2026-05-17T23:54:03.443778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aba13c36579ec357cfdfe59296a12c1d805aa53f1f6252dfb42c774f021e3c1

Aliases

arxiv: 1602.03155 · arxiv_version: 1602.03155v2 · doi: 10.48550/arxiv.1602.03155 · pith_short_12: HK5BHQ3FPHWD · pith_short_16: HK5BHQ3FPHWDK7H5 · pith_short_8: HK5BHQ3F

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/HK5BHQ3FPHWDK7H57ZMSS2QSYH \
  | 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: 3aba13c36579ec357cfdfe59296a12c1d805aa53f1f6252dfb42c774f021e3c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7883af3939e39a125226bba5201a5428b48a63428652218c5acb15e98c764c1a",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-02-09T20:22:46Z",
    "title_canon_sha256": "6da1be755bc740c420b481493263ba89e65416cd712aa873e6af675c13ac2a06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.03155",
    "kind": "arxiv",
    "version": 2
  }
}