Pith Number

pith:4B2OYL3V

pith:2015:4B2OYL3VKOPHXMJSITGPM2RGMI

not attested not anchored not stored refs pending

Propagation of exponential phase space singularities for Schr\"odinger equations with quadratic Hamiltonians

Evanthia Carypis, Patrik Wahlberg

arxiv:1510.00325 v3 · 2015-10-01 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4B2OYL3VKOPHXMJSITGPM2RGMI}

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	2026-05-18T01:17:30.543944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e074ec2f75539e7bb13244ccf66a26620bbd774b2bee37b4e7541474167b9c58

Aliases

arxiv: 1510.00325 · arxiv_version: 1510.00325v3 · doi: 10.48550/arxiv.1510.00325 · pith_short_12: 4B2OYL3VKOPH · pith_short_16: 4B2OYL3VKOPHXMJS · pith_short_8: 4B2OYL3V

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/4B2OYL3VKOPHXMJSITGPM2RGMI \
  | 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: e074ec2f75539e7bb13244ccf66a26620bbd774b2bee37b4e7541474167b9c58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da3dc377e29e954d0149440da409b58052072199e302fb9b9bc44805c8333d97",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-01T17:29:47Z",
    "title_canon_sha256": "6472087f09583f5cdeee2df5d65700c6d80628a689665d2086515dac6d1fa238"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00325",
    "kind": "arxiv",
    "version": 3
  }
}