Pith Number

pith:HX54JXU7

pith:2019:HX54JXU7J3N6RXTYSY3VAYFAUG

not attested not anchored not stored refs pending

Exponential asymptotics for the eigenvalues in the broken PT-symmetric region

Philippe H. Trinh, S. Jonathan Chapman

arxiv:1906.08218 v1 · 2019-06-19 · math-ph · math.CA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HX54JXU7J3N6RXTYSY3VAYFAUG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-17T23:42:54.286465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dfbc4de9f4edbe8de7896375060a0a1b03d435cffd7cb3f8f2ddafa9bf23457

Aliases

arxiv: 1906.08218 · arxiv_version: 1906.08218v1 · doi: 10.48550/arxiv.1906.08218 · pith_short_12: HX54JXU7J3N6 · pith_short_16: HX54JXU7J3N6RXTY · pith_short_8: HX54JXU7

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/HX54JXU7J3N6RXTYSY3VAYFAUG \
  | 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: 3dfbc4de9f4edbe8de7896375060a0a1b03d435cffd7cb3f8f2ddafa9bf23457

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4764565e6cc0e65a0c3dd51bcd3bc96871dd7d339e0c9557100c151b626da6c",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-06-19T16:50:02Z",
    "title_canon_sha256": "836892714de7cd7287277ef5eda148dd9527e1842fc5e73d1602c80e2e4f8fea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.08218",
    "kind": "arxiv",
    "version": 1
  }
}