Pith Number

pith:KFRGVVRI

pith:2005:KFRGVVRIEVDDQ3MK4P7WVID4VW

not attested not anchored not stored refs pending

Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation

Hong-yi Fan, Wei-Bo Gao

arxiv:math-ph/0512021 v1 · 2005-12-08 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KFRGVVRIEVDDQ3MK4P7WVID4VW}

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	2026-05-18T01:38:32.978275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51626ad6282546386d8ae3ff6aa07cad94cfec44bd68c861410217d1db3b9bff

Aliases

arxiv: math-ph/0512021 · arxiv_version: math-ph/0512021v1 · doi: 10.48550/arxiv.math-ph/0512021 · pith_short_12: KFRGVVRIEVDD · pith_short_16: KFRGVVRIEVDDQ3MK · pith_short_8: KFRGVVRI

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/KFRGVVRIEVDDQ3MK4P7WVID4VW \
  | 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: 51626ad6282546386d8ae3ff6aa07cad94cfec44bd68c861410217d1db3b9bff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad10947ef24ccba0579d820a84e223d7d3fba31d5e0c18c8ecfb51de013dcb72",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-12-08T05:53:57Z",
    "title_canon_sha256": "facbf27547c80526a9afeaee5446ce3ff286fa4bb5a829e93e052e9d3848e92b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0512021",
    "kind": "arxiv",
    "version": 1
  }
}