Pith Number

pith:GL4UIHGI

pith:2009:GL4UIHGIXOV626PWCTKGF2ZF6W

not attested not anchored not stored refs pending

PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues

Carl M. Bender, Philip D. Mannheim

arxiv:0902.1365 v1 · 2009-02-09 · hep-th · 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{GL4UIHGIXOV626PWCTKGF2ZF6W}

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	2026-05-18T02:35:01.263638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32f9441cc8bbabed79f614d462eb25f5b25712b6d74ae97d0a52d5e9ddc8b60e

Aliases

arxiv: 0902.1365 · arxiv_version: 0902.1365v1 · doi: 10.48550/arxiv.0902.1365 · pith_short_12: GL4UIHGIXOV6 · pith_short_16: GL4UIHGIXOV626PW · pith_short_8: GL4UIHGI

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/GL4UIHGIXOV626PWCTKGF2ZF6W \
  | 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: 32f9441cc8bbabed79f614d462eb25f5b25712b6d74ae97d0a52d5e9ddc8b60e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e77f5a9dc7c1c875cb94b48469ea9579fcfbcd25acf921e651260c7a9f2b108",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2009-02-09T05:01:18Z",
    "title_canon_sha256": "7349bc6ca548cfc7ca2ecc0d83fdde84b3339310b66c056fdc2a579e9d5e085f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1365",
    "kind": "arxiv",
    "version": 1
  }
}