Pith Number

pith:QDH26XO4

pith:2011:QDH26XO4KYMFUVAINQOPW3NU6T

not attested not anchored not stored refs pending

Interaction Morawetz estimate for the magnetic Schr\"odinger equation and applications

James Colliander, Jeonghun Lee, Magdalena Czubak

arxiv:1112.4452 v2 · 2011-12-19 · 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{QDH26XO4KYMFUVAINQOPW3NU6T}

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	2026-05-18T02:54:13.027868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80cfaf5ddc56185a54086c1cfb6db4f4dd2266d1da13401eaf05eaa95e328dad

Aliases

arxiv: 1112.4452 · arxiv_version: 1112.4452v2 · doi: 10.48550/arxiv.1112.4452 · pith_short_12: QDH26XO4KYMF · pith_short_16: QDH26XO4KYMFUVAI · pith_short_8: QDH26XO4

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/QDH26XO4KYMFUVAINQOPW3NU6T \
  | 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: 80cfaf5ddc56185a54086c1cfb6db4f4dd2266d1da13401eaf05eaa95e328dad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdd5a140efde7db544df7a756f662dcfa4164e4e558a38101c44f4fb91e91d36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-19T20:08:10Z",
    "title_canon_sha256": "9a96f7b94908c44151237a493a7dbf3381f3af056798db6c25e1287caa64a5ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4452",
    "kind": "arxiv",
    "version": 2
  }
}