Pith Number

pith:P7V65UQA

pith:2025:P7V65UQA3EF4NVD4JCDPEP7Z2T

not attested not anchored not stored refs pending

On the lattice property of the Koopman operator spectrum

Jason J. Bramburger

arxiv:2507.23498 v1 · 2025-07-31 · math.DS · math.FA · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P7V65UQA3EF4NVD4JCDPEP7Z2T}

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	2026-07-05T11:46:25.374011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7febeed200d90bc6d47c4886f23ff9d4cff0784fa8f2d479d9ecc6f81e26b4aa

Aliases

arxiv: 2507.23498 · arxiv_version: 2507.23498v1 · doi: 10.48550/arxiv.2507.23498 · pith_short_12: P7V65UQA3EF4 · pith_short_16: P7V65UQA3EF4NVD4 · pith_short_8: P7V65UQA

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/P7V65UQA3EF4NVD4JCDPEP7Z2T \
  | 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: 7febeed200d90bc6d47c4886f23ff9d4cff0784fa8f2d479d9ecc6f81e26b4aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ed32b2222eb431d5de916925b8c281f46a7d283e2afb4df8f01181d37ddf041",
    "cross_cats_sorted": [
      "math.FA",
      "nlin.CD"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-07-31T12:38:39Z",
    "title_canon_sha256": "542708b6c5f4539394ff13d250b4bb8edaa02a46fa73c316a75a637ee3dc4da4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.23498",
    "kind": "arxiv",
    "version": 1
  }
}