Pith Number

pith:AE4JZTKF

pith:2013:AE4JZTKFR64QV2KP47K4AQKAVW

not attested not anchored not stored refs pending

Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3

Frederic Bernicot, Pierre Germain

arxiv:1310.3659 v1 · 2013-10-14 · 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{AE4JZTKFR64QV2KP47K4AQKAVW}

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	2026-05-18T01:47:05.812998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01389ccd458fb90ae94fe7d5c04140adb4a8916bd2245332be69899e330c2bb3

Aliases

arxiv: 1310.3659 · arxiv_version: 1310.3659v1 · doi: 10.48550/arxiv.1310.3659 · pith_short_12: AE4JZTKFR64Q · pith_short_16: AE4JZTKFR64QV2KP · pith_short_8: AE4JZTKF

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/AE4JZTKFR64QV2KP47K4AQKAVW \
  | 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: 01389ccd458fb90ae94fe7d5c04140adb4a8916bd2245332be69899e330c2bb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a96ef8609fe398cb88d9722e3557bc4fdc131951c4411dde3b79ffd8da745c38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-10-14T12:48:44Z",
    "title_canon_sha256": "75750176683a5bc7b235a77c1974b1e432ddc52296891151749d665d33ab3b4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.3659",
    "kind": "arxiv",
    "version": 1
  }
}