Pith Number

pith:SU2DB4XW

pith:2010:SU2DB4XW3M766ZA67L2W5I7AHM

not attested not anchored not stored refs pending

On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces

Alexandru D. Ionescu, Benoit Pausader, Gigliola Staffilani

arxiv:1008.1237 v2 · 2010-08-06 · 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{SU2DB4XW3M766ZA67L2W5I7AHM}

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	2026-05-18T04:41:14.978688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

953430f2f6db3fef641efaf56ea3e03b1eec8def57503cefa917269ab6f475ec

Aliases

arxiv: 1008.1237 · arxiv_version: 1008.1237v2 · doi: 10.48550/arxiv.1008.1237 · pith_short_12: SU2DB4XW3M76 · pith_short_16: SU2DB4XW3M766ZA6 · pith_short_8: SU2DB4XW

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/SU2DB4XW3M766ZA67L2W5I7AHM \
  | 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: 953430f2f6db3fef641efaf56ea3e03b1eec8def57503cefa917269ab6f475ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c4b5efd2c74669ced53b71d5d4173680880a70e77ab948f1c84d0f269d4a141",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-08-06T17:01:37Z",
    "title_canon_sha256": "4f772cebc0ee399a8cf6e8c4641f22d30b1fb4fe06804b64b63d0514a7ccced7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1237",
    "kind": "arxiv",
    "version": 2
  }
}