Pith Number

pith:4X5RE4DX

pith:2009:4X5RE4DX7E26IIP5XNSTE6Q67B

not attested not anchored not stored refs pending

Scattering theory below energy for the cubic fourth-order Schr\"{o}dinger equation

Changxing Miao, Haigen Wu, Junyong Zhang

arxiv:0907.5047 v3 · 2009-07-29 · math.AP · math-ph · 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{4X5RE4DX7E26IIP5XNSTE6Q67B}

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	2026-05-18T02:18:01.952613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5fb127077f935e421fdbb65327a1ef840e149487d15510798765d897deed4f7

Aliases

arxiv: 0907.5047 · arxiv_version: 0907.5047v3 · doi: 10.48550/arxiv.0907.5047 · pith_short_12: 4X5RE4DX7E26 · pith_short_16: 4X5RE4DX7E26IIP5 · pith_short_8: 4X5RE4DX

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/4X5RE4DX7E26IIP5XNSTE6Q67B \
  | 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: e5fb127077f935e421fdbb65327a1ef840e149487d15510798765d897deed4f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99a6df9b5f9c26318247069cb04a9b284ce72c194f8cce32d448d3b5dfe8aace",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-07-29T04:58:55Z",
    "title_canon_sha256": "c15db166f7a203f21ee903cc2c864e08b80e1a621bb50544f4744388c4b61f74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5047",
    "kind": "arxiv",
    "version": 3
  }
}