Pith Number

pith:Y2VJZB7I

pith:2026:Y2VJZB7I32Z3ZELI6K7H3MMQFF

not attested not anchored not stored refs pending

Eigenvalue asymptotics for the one-particle density matrix and one-particle kinetic energy density operator

Alexander V. Sobolev, S{\o}ren Fournais

arxiv:2608.09570 v1 · 2026-08-10 · math-ph · math.FA · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y2VJZB7I32Z3ZELI6K7H3MMQFF}

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	2026-08-11T02:24:31.354831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6aa9c87e8deb3bc9168f2be7db1902961453d22540493d7ef81394b31c0578a

Aliases

arxiv: 2608.09570 · arxiv_version: 2608.09570v1 · doi: 10.48550/arxiv.2608.09570 · pith_short_12: Y2VJZB7I32Z3 · pith_short_16: Y2VJZB7I32Z3ZELI · pith_short_8: Y2VJZB7I

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/Y2VJZB7I32Z3ZELI6K7H3MMQFF \
  | 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: c6aa9c87e8deb3bc9168f2be7db1902961453d22540493d7ef81394b31c0578a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36a5d96c456b2b7639044f9ad3945f2e533c0cc8aa44f104ec959a859712e69e",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-08-10T13:07:18Z",
    "title_canon_sha256": "6d2b1faaa10ddc940f05c77dc50345fa5a78bc8ea3209c98539feb9988b2fe57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09570",
    "kind": "arxiv",
    "version": 1
  }
}