Pith Number

pith:XCB7IT5S

pith:2012:XCB7IT5SX4PGJX4OTPONLFMCXE

not attested not anchored not stored refs pending

The defocusing $\dot{H}^{1/2}$-critical NLS in high dimensions

Jason Murphy

arxiv:1212.6816 v1 · 2012-12-31 · 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{XCB7IT5SX4PGJX4OTPONLFMCXE}

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	2026-05-18T02:29:23.733519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b883f44fb2bf1e64df8e9bdcd59582b92bdd9f0c0f6ace1188227667b120f493

Aliases

arxiv: 1212.6816 · arxiv_version: 1212.6816v1 · doi: 10.48550/arxiv.1212.6816 · pith_short_12: XCB7IT5SX4PG · pith_short_16: XCB7IT5SX4PGJX4O · pith_short_8: XCB7IT5S

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/XCB7IT5SX4PGJX4OTPONLFMCXE \
  | 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: b883f44fb2bf1e64df8e9bdcd59582b92bdd9f0c0f6ace1188227667b120f493

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63f93c0e2110605a805e0fe1b5ec7d2a9fbc3b73e7f06f5d37cedbe5b16c3e71",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-31T04:33:12Z",
    "title_canon_sha256": "30e21dddba38deed3d9917fcbbf13f15a07186ab42f4d7a03d0b411e93ed6376"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6816",
    "kind": "arxiv",
    "version": 1
  }
}