Pith Number

pith:GPN3MM3O

pith:2026:GPN3MM3OMAV52PBE7HZJ7SLFXL

not attested not anchored not stored refs pending

The spectral edge of the quartic SYK model

Yukun He

arxiv:2607.18998 v1 · 2026-07-21 · math-ph · hep-th · math.MP · math.OA · 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{GPN3MM3OMAV52PBE7HZJ7SLFXL}

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	2026-07-22T01:24:03.758080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33dbb6336e602bdd3c24f9f29fc965badcf1f1cdeecc2bd4fa0d10394636a821

Aliases

arxiv: 2607.18998 · arxiv_version: 2607.18998v1 · doi: 10.48550/arxiv.2607.18998 · pith_short_12: GPN3MM3OMAV5 · pith_short_16: GPN3MM3OMAV52PBE · pith_short_8: GPN3MM3O

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/GPN3MM3OMAV52PBE7HZJ7SLFXL \
  | 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: 33dbb6336e602bdd3c24f9f29fc965badcf1f1cdeecc2bd4fa0d10394636a821

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec8e70828e0be073f8bbd35f7e0657b9fc9e70029495065105998668c6823e4e",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "math.OA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-21T11:32:10Z",
    "title_canon_sha256": "0d67cadebea6e63a48659f68b226822c92260a55fa79180c822330a58e82ee48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18998",
    "kind": "arxiv",
    "version": 1
  }
}