Pith Number

pith:PJHYVPRG

pith:2026:PJHYVPRGZUKLH7T7IYWGK4BUXF

not attested not anchored not stored refs pending

PhaseJumps: fast computation of zeros from planar grid samples

Antti Haimi, G\"unther Koliander, Jos\'e Luis Romero

arxiv:2603.13158 v2 · 2026-03-13 · math.NA · cs.NA · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJHYVPRGZUKLH7T7IYWGK4BUXF}

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	2026-07-03T01:17:18.541907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a4f8abe26cd14b3fe7f462c657034b94e106c283d25dae9f4dc159e25d44eeb

Aliases

arxiv: 2603.13158 · arxiv_version: 2603.13158v2 · doi: 10.48550/arxiv.2603.13158 · pith_short_12: PJHYVPRGZUKL · pith_short_16: PJHYVPRGZUKLH7T7 · pith_short_8: PJHYVPRG

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/PJHYVPRGZUKLH7T7IYWGK4BUXF \
  | 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: 7a4f8abe26cd14b3fe7f462c657034b94e106c283d25dae9f4dc159e25d44eeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c28b80065821bed5b70008bb3261554875701bd9052ca927155d4d69da29ba17",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-03-13T16:51:11Z",
    "title_canon_sha256": "3d0615ba64744f1b8c0220efc3cb22d347cf0ad5eb26dadccc53d555928d5634"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.13158",
    "kind": "arxiv",
    "version": 2
  }
}