Pith Number

pith:QZFKHOWT

pith:2019:QZFKHOWTX2SP5FXPPTQYUM7LGS

not attested not anchored not stored refs pending

Spectral rigidity of random Schr\"odinger operators via Feynman-Kac formulas

Pierre Yves Gaudreau Lamarre, Promit Ghosal, Yuchen Liao

arxiv:1908.08422 v2 · 2019-08-22 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QZFKHOWTX2SP5FXPPTQYUM7LGS}

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	2026-07-05T01:09:38.991253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

864aa3bad3bea4fe96ef7ce18a33eb34ad0bc1e97a13494012d8b3f2ef2db8c8

Aliases

arxiv: 1908.08422 · arxiv_version: 1908.08422v2 · doi: 10.48550/arxiv.1908.08422 · pith_short_12: QZFKHOWTX2SP · pith_short_16: QZFKHOWTX2SP5FXP · pith_short_8: QZFKHOWT

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/QZFKHOWTX2SP5FXPPTQYUM7LGS \
  | 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: 864aa3bad3bea4fe96ef7ce18a33eb34ad0bc1e97a13494012d8b3f2ef2db8c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ea68fcabfb5e0c8cf8c8043ceecd835fbf90f06b14c4f2b2aa4231dd098f3fe",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-08-22T14:58:48Z",
    "title_canon_sha256": "0ab90cf7ec81f0b71e9cb459b696b83281136b35b176c47d8529589ead17993c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08422",
    "kind": "arxiv",
    "version": 2
  }
}