Pith Number

pith:67HN3EY6

pith:2026:67HN3EY6GKGG4YSFFLOB46XEY5

not attested not anchored not stored refs pending

The Ultimate Ishii-Pastur Theorem for Whole-Line Ergodic Block Jacobi Operators

Bei Zhang, Qi Zhou, Zhenfu Wang

arxiv:2607.25808 v1 · 2026-07-28 · math.SP · math-ph · math.DS · 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{67HN3EY6GKGG4YSFFLOB46XEY5}

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	2026-07-29T01:26:03.931978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7cedd931e328c6e62452adc1e7ae4c765f7b7f8cabeebb2e62026ecabc8c3ff

Aliases

arxiv: 2607.25808 · arxiv_version: 2607.25808v1 · doi: 10.48550/arxiv.2607.25808 · pith_short_12: 67HN3EY6GKGG · pith_short_16: 67HN3EY6GKGG4YSF · pith_short_8: 67HN3EY6

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/67HN3EY6GKGG4YSFFLOB46XEY5 \
  | 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: f7cedd931e328c6e62452adc1e7ae4c765f7b7f8cabeebb2e62026ecabc8c3ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb946cefda314bc7d1d498acdfeff94c0c129ddd82b4e09cc4255a9c7c49aa57",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-07-28T14:55:36Z",
    "title_canon_sha256": "75cc5aae9c38e4206bded0b8d065ed301b32f705d563b80d89987414e5e24849"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25808",
    "kind": "arxiv",
    "version": 1
  }
}