Pith Number

pith:AA22UYPT

pith:2010:AA22UYPTI6ILA7HKON3HSBIBUQ

not attested not anchored not stored refs pending

Sub-criticality of non-local Schr\"odinger systems with antisymmetric potentials and applications to half-harmonic maps

Francesca Da Lio, Tristan Riviere

arxiv:1012.2438 v1 · 2010-12-11 · 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{AA22UYPTI6ILA7HKON3HSBIBUQ}

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	2026-05-18T04:33:28.631696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0035aa61f34790b07cea7376790501a4116d7600876d9d9f3ff9c885ee45c882

Aliases

arxiv: 1012.2438 · arxiv_version: 1012.2438v1 · doi: 10.48550/arxiv.1012.2438 · pith_short_12: AA22UYPTI6IL · pith_short_16: AA22UYPTI6ILA7HK · pith_short_8: AA22UYPT

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/AA22UYPTI6ILA7HKON3HSBIBUQ \
  | 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: 0035aa61f34790b07cea7376790501a4116d7600876d9d9f3ff9c885ee45c882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d2328cda14d2fd73c5fb96228ef42727ee787503b3ca34e46df1e655b0ca8bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-11T09:04:54Z",
    "title_canon_sha256": "1ced8f9dc1ef387f0f866e464b5bada202b0e2af326d6ae284b79dc41728f161"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2438",
    "kind": "arxiv",
    "version": 1
  }
}