Pith Number

pith:4DNFFBVI

pith:2026:4DNFFBVIFPZ3Q3IGBWQGENZOKI

not attested not anchored not stored refs pending

Isospectrality and Operator Complexity

Natan Andrei, Pradip Kattel, Yicheng Tang

arxiv:2606.05294 v1 · 2026-06-03 · quant-ph · cond-mat.stat-mech · cond-mat.str-el · cond-mat.supr-con · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4DNFFBVIFPZ3Q3IGBWQGENZOKI}

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	2026-06-05T00:13:52.240841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0da5286a82bf3b86d060da062372e520e38eb7b65833bea684b00f471aa5f69

Aliases

arxiv: 2606.05294 · arxiv_version: 2606.05294v1 · doi: 10.48550/arxiv.2606.05294 · pith_short_12: 4DNFFBVIFPZ3 · pith_short_16: 4DNFFBVIFPZ3Q3IG · pith_short_8: 4DNFFBVI

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/4DNFFBVIFPZ3Q3IGBWQGENZOKI \
  | 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: e0da5286a82bf3b86d060da062372e520e38eb7b65833bea684b00f471aa5f69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3762146cda1a2939553248065b0774529b5f6a02bb808f4f922dddf1d292a5b",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cond-mat.str-el",
      "cond-mat.supr-con",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-06-03T18:00:05Z",
    "title_canon_sha256": "400884bee4b90af709b0829ccfe90b02ea992f71df2713b2706b6626e80df6eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05294",
    "kind": "arxiv",
    "version": 1
  }
}