Pith Number

pith:OZKAU4ZA

pith:2012:OZKAU4ZA4HRVRLMLHMMES3L4GA

not attested not anchored not stored refs pending

Parametrix for wave equations on a rough background I: regularity of the phase at initial time

Jeremie Szeftel

arxiv:1204.1768 v1 · 2012-04-08 · math.AP · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZKAU4ZA4HRVRLMLHMMES3L4GA}

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	2026-05-18T03:58:15.244098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76540a7320e1e358ad8b3b18496d7c30105cf7e72d7e0874107b1aa3a29cb8f3

Aliases

arxiv: 1204.1768 · arxiv_version: 1204.1768v1 · doi: 10.48550/arxiv.1204.1768 · pith_short_12: OZKAU4ZA4HRV · pith_short_16: OZKAU4ZA4HRVRLML · pith_short_8: OZKAU4ZA

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/OZKAU4ZA4HRVRLMLHMMES3L4GA \
  | 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: 76540a7320e1e358ad8b3b18496d7c30105cf7e72d7e0874107b1aa3a29cb8f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6e66a5d7eed6710c0785cdb881474c8ea55fd9c4b566d0158d5324235beb2b0",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-08T23:12:18Z",
    "title_canon_sha256": "229710672bb8b652de37ad6206bba79eb21171ea7d6fd848cdde1a532fc666bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1768",
    "kind": "arxiv",
    "version": 1
  }
}