Pith Number

pith:TPY5EBXF

pith:2016:TPY5EBXFPBOM6D4KUFVHZQNKOY

not attested not anchored not stored refs pending

Gibbs states defined by biorthogonal sequences

Camillo TRapani, Fabio Bagarello, Salvatore Triolo

arxiv:1609.00660 v1 · 2016-09-02 · math-ph · math.MP · 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{TPY5EBXFPBOM6D4KUFVHZQNKOY}

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.

Cited by

1 paper in Pith

Kubo-Martin-Schwinger conditions for non-Hermitian systems

Receipt and verification

First computed	2026-05-18T01:02:36.845037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bf1d206e5785ccf0f8aa16a7cc1aa7606a20a95b19230424d184a86b8584a46

Aliases

arxiv: 1609.00660 · arxiv_version: 1609.00660v1 · doi: 10.48550/arxiv.1609.00660 · pith_short_12: TPY5EBXFPBOM · pith_short_16: TPY5EBXFPBOM6D4K · pith_short_8: TPY5EBXF

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/TPY5EBXFPBOM6D4KUFVHZQNKOY \
  | 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: 9bf1d206e5785ccf0f8aa16a7cc1aa7606a20a95b19230424d184a86b8584a46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6a18df4255f7f70e8c61a1d623425fd2fa30586ae06f11cbc844041be8702ef",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-09-02T16:47:59Z",
    "title_canon_sha256": "023c6633a5721c69e982627126bac3126f9a0bfb5bcd78ad91c3718be537897a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00660",
    "kind": "arxiv",
    "version": 1
  }
}