Pith Number

pith:DZ45EA2V

pith:2013:DZ45EA2VYPGWD2VOIRTMVMVVJL

not attested not anchored not stored refs pending

Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities

Lechao Xiao

arxiv:1311.3725 v2 · 2013-11-15 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZ45EA2VYPGWD2VOIRTMVMVVJL}

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	2026-05-18T01:20:26.621139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e79d20355c3cd61eaae4466cab2b54afd47a2c06e142211c2e8b77a719ef310

Aliases

arxiv: 1311.3725 · arxiv_version: 1311.3725v2 · doi: 10.48550/arxiv.1311.3725 · pith_short_12: DZ45EA2VYPGW · pith_short_16: DZ45EA2VYPGWD2VO · pith_short_8: DZ45EA2V

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/DZ45EA2VYPGWD2VOIRTMVMVVJL \
  | 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: 1e79d20355c3cd61eaae4466cab2b54afd47a2c06e142211c2e8b77a719ef310

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d902ebf0d88f842a6f3a3669b01180446fac9a489e63f247c4d9b9f2d70858fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-11-15T04:29:03Z",
    "title_canon_sha256": "9ddae83a409bf165f3fa84c031e050d6f12c62982a065931f5404ccd97b067a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3725",
    "kind": "arxiv",
    "version": 2
  }
}