Pith Number

pith:TDCBKPG5

pith:2013:TDCBKPG5KY57XGENE2YNXCQE56

not attested not anchored not stored refs pending

The real spectrum of the imaginary cubic oscillator: An expository proof

Gian Michele Graf, Ilario Giordanelli

arxiv:1310.7767 v2 · 2013-10-29 · 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{TDCBKPG5KY57XGENE2YNXCQE56}

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	2026-05-18T02:56:19.022196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98c4153cdd563bfb988d26b0db8a04ef9c3e8573b0455994a82219e1445c4eb6

Aliases

arxiv: 1310.7767 · arxiv_version: 1310.7767v2 · doi: 10.48550/arxiv.1310.7767 · pith_short_12: TDCBKPG5KY57 · pith_short_16: TDCBKPG5KY57XGEN · pith_short_8: TDCBKPG5

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/TDCBKPG5KY57XGENE2YNXCQE56 \
  | 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: 98c4153cdd563bfb988d26b0db8a04ef9c3e8573b0455994a82219e1445c4eb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "397bdd21787b962301e8681c8fb170030ed55250e8e1f56fea219d58cd9239b9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-10-29T11:46:45Z",
    "title_canon_sha256": "5052a7d138de9fe3afe81521813be9a88a2424c1c13fd84aa5874eea8d0bc178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7767",
    "kind": "arxiv",
    "version": 2
  }
}