Pith Number

pith:74K4DD3Q

pith:2012:74K4DD3QRCQXIBPVJNVNERWXE6

not attested not anchored not stored refs pending

Parametrix for wave equations on a rough background III: space-time regularity of the phase

Jeremie Szeftel

arxiv:1204.1770 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{74K4DD3QRCQXIBPVJNVNERWXE6}

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	2026-05-18T03:58:15.226745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff15c18f7088a17405f54b6ad246d727a5668e003b6cba972fb163284d633170

Aliases

arxiv: 1204.1770 · arxiv_version: 1204.1770v1 · doi: 10.48550/arxiv.1204.1770 · pith_short_12: 74K4DD3QRCQX · pith_short_16: 74K4DD3QRCQXIBPV · pith_short_8: 74K4DD3Q

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/74K4DD3QRCQXIBPVJNVNERWXE6 \
  | 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: ff15c18f7088a17405f54b6ad246d727a5668e003b6cba972fb163284d633170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b6e20485fc29c750d807046814ec5f6a56e0b186c456efbf15921cb4e285a15",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-08T23:19:17Z",
    "title_canon_sha256": "97d5cabd646babd4bc4fbe81167ae85848d9084c46df6a3babb1ee7da7cefd55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1770",
    "kind": "arxiv",
    "version": 1
  }
}