Pith Number

pith:23C7Q4EX

pith:2012:23C7Q4EXIQ6YWHFUJ2RMKGVS4J

not attested not anchored not stored refs pending

Inter-critical NLS: critical $\dot{H}^s$-bounds imply scattering

Jason Murphy

arxiv:1209.4582 v1 · 2012-09-20 · 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{23C7Q4EXIQ6YWHFUJ2RMKGVS4J}

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	2026-05-18T02:29:23.747785Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6c5f87097443d8b1cb44ea2c51ab2e26cd04ef956c4f16959b78564980c8203

Aliases

arxiv: 1209.4582 · arxiv_version: 1209.4582v1 · doi: 10.48550/arxiv.1209.4582 · pith_short_12: 23C7Q4EXIQ6Y · pith_short_16: 23C7Q4EXIQ6YWHFU · pith_short_8: 23C7Q4EX

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/23C7Q4EXIQ6YWHFUJ2RMKGVS4J \
  | 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: d6c5f87097443d8b1cb44ea2c51ab2e26cd04ef956c4f16959b78564980c8203

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3393d5a7c8c95fc07047f1aa90377d3c1663ddd91eb30452b3d716d241fab039",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-20T16:51:48Z",
    "title_canon_sha256": "12c88d2bee43ad32172f8cdd0c1aef1018fc0023591fd9df5e510838ef6b34b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4582",
    "kind": "arxiv",
    "version": 1
  }
}