Pith Number

pith:XSY7HH5W

pith:2015:XSY7HH5WLXYHS6BO2TH6P7LHPL

not attested not anchored not stored refs pending

Concentration and non-concentration for the Schr\"odinger evolution on Zoll manifolds

Fabricio Maci\`a, Gabriel Rivi\`ere

arxiv:1505.04945 v1 · 2015-05-19 · math.AP · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XSY7HH5WLXYHS6BO2TH6P7LHPL}

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	2026-05-18T02:05:22.692526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcb1f39fb65df079782ed4cfe7fd677ac04931c7820a2b0e0caa3442d5ef3712

Aliases

arxiv: 1505.04945 · arxiv_version: 1505.04945v1 · doi: 10.48550/arxiv.1505.04945 · pith_short_12: XSY7HH5WLXYH · pith_short_16: XSY7HH5WLXYHS6BO · pith_short_8: XSY7HH5W

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/XSY7HH5WLXYHS6BO2TH6P7LHPL \
  | 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: bcb1f39fb65df079782ed4cfe7fd677ac04931c7820a2b0e0caa3442d5ef3712

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "632aceb58fab2df9ff6cab59eeeb9e8540436db7d6cc44b703a6a56838de25ad",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-05-19T10:28:50Z",
    "title_canon_sha256": "1aa547c313c087257eb441a17f33214830a20794465dc15841a47e066e122c11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04945",
    "kind": "arxiv",
    "version": 1
  }
}