Pith Number

pith:ZATYHSH5

pith:2006:ZATYHSH5RVLVAGTSWXA4FGXLAI

not attested not anchored not stored refs pending

Uniform existence of the integrated density of states for random Schr\"odinger operators on metric graphs over $\mathbb{Z}^d$

Daniel H. Lenz, Ivan Veseli\'c, Michael J. Gruber

arxiv:math/0612743 v2 · 2006-12-23 · math.SP · 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{ZATYHSH5RVLVAGTSWXA4FGXLAI}

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	2026-05-18T04:08:53.028019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c82783c8fd8d57501a72b5c1c29aeb022b9263583efaefab8c78ef5dc3326f5f

Aliases

arxiv: math/0612743 · arxiv_version: math/0612743v2 · doi: 10.48550/arxiv.math/0612743 · pith_short_12: ZATYHSH5RVLV · pith_short_16: ZATYHSH5RVLVAGTS · pith_short_8: ZATYHSH5

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/ZATYHSH5RVLVAGTSWXA4FGXLAI \
  | 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: c82783c8fd8d57501a72b5c1c29aeb022b9263583efaefab8c78ef5dc3326f5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b48e52262ba8908a28d0141ab3fd5e2c5e8925a06f4d39dac970b9c962068e3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2006-12-23T13:41:33Z",
    "title_canon_sha256": "0f6607865eed263b5eba75d2a3a2e1a280caa09d2ec7347f9cc451727e1d7e98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612743",
    "kind": "arxiv",
    "version": 2
  }
}