Pith Number

pith:WR5VY5G5

pith:2009:WR5VY5G52YZ4RQWIFATCAQXX2E

not attested not anchored not stored refs pending

Minimal blow-up solutions to the mass-critical inhomogeneous NLS equation

R\'emi Carles (I3M), Thomas Duyckaerts (AGM), Valeria Banica (DP)

arxiv:0904.1317 v2 · 2009-04-08 · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WR5VY5G52YZ4RQWIFATCAQXX2E}

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	2026-05-18T04:12:43.176517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b47b5c74ddd633c8c2c828262042f7d12a567272580596bbdde265bbf1d928e7

Aliases

arxiv: 0904.1317 · arxiv_version: 0904.1317v2 · doi: 10.48550/arxiv.0904.1317 · pith_short_12: WR5VY5G52YZ4 · pith_short_16: WR5VY5G52YZ4RQWI · pith_short_8: WR5VY5G5

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/WR5VY5G52YZ4RQWIFATCAQXX2E \
  | 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: b47b5c74ddd633c8c2c828262042f7d12a567272580596bbdde265bbf1d928e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "278f85b0e1e15fc529e88abe81e516eff2a8d34e27e62bf95e1b2d5fcbe0c050",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-04-08T18:34:32Z",
    "title_canon_sha256": "96f04274527ff0f46a1cc73b7223dadd978ba26d018c54d62ee7203c4925a563"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.1317",
    "kind": "arxiv",
    "version": 2
  }
}