Pith Number

pith:Y5CWAUVH

pith:2016:Y5CWAUVHLR3H23AYX64DDBJWBL

not attested not anchored not stored refs pending

Dyson's spike for random Schroedinger operators and Novikov-Shubin invariants of groups

B\'alint Vir\'ag, Marcin Kotowski

arxiv:1602.06626 v1 · 2016-02-22 · math.PR · math-ph · math.GR · 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{Y5CWAUVHLR3H23AYX64DDBJWBL}

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	2026-05-18T00:26:16.751877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7456052a75c767d6c18bfb83185360ac5a9841c69ac2b08e0c773585ea0bbf0

Aliases

arxiv: 1602.06626 · arxiv_version: 1602.06626v1 · doi: 10.48550/arxiv.1602.06626 · pith_short_12: Y5CWAUVHLR3H · pith_short_16: Y5CWAUVHLR3H23AY · pith_short_8: Y5CWAUVH

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/Y5CWAUVHLR3H23AYX64DDBJWBL \
  | 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: c7456052a75c767d6c18bfb83185360ac5a9841c69ac2b08e0c773585ea0bbf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25e4dbb0f6f0a83174b8e9770613a80879696f2c28290f6ffef4a2767d18de77",
    "cross_cats_sorted": [
      "math-ph",
      "math.GR",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-02-22T02:09:49Z",
    "title_canon_sha256": "850996693963d75ef966fd432641c2e781f199872d539e247ee58cb761f76197"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.06626",
    "kind": "arxiv",
    "version": 1
  }
}