Pith Number

pith:NUH663PF

pith:2026:NUH663PFV7AHTRGRBZBWDMJVAN

not attested not anchored not stored refs pending

Metric completion of the Bender--Brody--M\"uller Hamiltonian: dilation spectrum and missing eigenstates

Kejun Liu

arxiv:2607.19067 v1 · 2026-07-21 · math-ph · math.MP · math.SP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NUH663PFV7AHTRGRBZBWDMJVAN}

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	2026-07-22T01:24:07.093011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d0fef6de5afc079c4d10e4361b13503451d714615c0b68532da1a0fc4301429

Aliases

arxiv: 2607.19067 · arxiv_version: 2607.19067v1 · doi: 10.48550/arxiv.2607.19067 · pith_short_12: NUH663PFV7AH · pith_short_16: NUH663PFV7AHTRGR · pith_short_8: NUH663PF

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/NUH663PFV7AHTRGRBZBWDMJVAN \
  | 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: 6d0fef6de5afc079c4d10e4361b13503451d714615c0b68532da1a0fc4301429

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "699765881776b0a186c2f6464307bfb4b5f71ec46c2ebf6830905dcc1c092af4",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-21T12:58:24Z",
    "title_canon_sha256": "d8ea0b13b4ae7655d2e20e1f310271d696afd5b11ee73e9d96bf46dbce48debb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19067",
    "kind": "arxiv",
    "version": 1
  }
}