Pith Number

pith:C545VDHC

pith:2013:C545VDHC665OZ62LF7CTM3FGSA

not attested not anchored not stored refs pending

Control for Schr\"odinger equations on 2-tori: rough potentials

Jean Bourgain, Maciej Zworski, Nicolas Burq

arxiv:1301.1282 v1 · 2013-01-07 · math.AP · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C545VDHC665OZ62LF7CTM3FGSA}

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	2026-05-18T03:37:06.312995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1779da8ce2f7baecfb4b2fc5366ca6900a93ddd1ed065ea67533d6e34c7eb5e4

Aliases

arxiv: 1301.1282 · arxiv_version: 1301.1282v1 · doi: 10.48550/arxiv.1301.1282 · pith_short_12: C545VDHC665O · pith_short_16: C545VDHC665OZ62L · pith_short_8: C545VDHC

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/C545VDHC665OZ62LF7CTM3FGSA \
  | 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: 1779da8ce2f7baecfb4b2fc5366ca6900a93ddd1ed065ea67533d6e34c7eb5e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77fc4b2f73d7e9e1f3d28f25eea74a53dc625ba31b974add1252d3ff7553f744",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-07T17:43:25Z",
    "title_canon_sha256": "7adafc6b06f3ecdbacfa7d035fc1abda1a787373494978f5c0bd5bc38187bf71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1282",
    "kind": "arxiv",
    "version": 1
  }
}