Pith Number

pith:A4RETU5N

pith:2013:A4RETU5N7NSEE6GZU4HKSWAVM3

not attested not anchored not stored refs pending

Dispersive estimates for four dimensional Schr\"{o}dinger and wave equations with obstructions at zero energy

M. Burak Erdogan, Michael Goldberg, William R. Green

arxiv:1310.6302 v1 · 2013-10-23 · 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{A4RETU5N7NSEE6GZU4HKSWAVM3}

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	2026-05-18T02:42:06.107895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

072249d3adfb644278d9a70ea9581566c2261c0acdf36de94b5a69e44f3b3525

Aliases

arxiv: 1310.6302 · arxiv_version: 1310.6302v1 · doi: 10.48550/arxiv.1310.6302 · pith_short_12: A4RETU5N7NSE · pith_short_16: A4RETU5N7NSEE6GZ · pith_short_8: A4RETU5N

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/A4RETU5N7NSEE6GZU4HKSWAVM3 \
  | 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: 072249d3adfb644278d9a70ea9581566c2261c0acdf36de94b5a69e44f3b3525

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ddb27fbcb6ef185e220c5cf5b8b7ef3d85c1b941fb30b4c60bfc0214d0084a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-10-23T17:30:21Z",
    "title_canon_sha256": "3ea96a367db5adef697e8375d11aa9106b3beb80c6b596ec1b408e8e297bf5cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6302",
    "kind": "arxiv",
    "version": 1
  }
}