Pith Number

pith:4URIJ64P

pith:2026:4URIJ64PYMPOLGC6XXGW7XH6OF

not attested not anchored not stored refs pending

Classification of singularities of planar slowness surfaces

Antonio Cocan, Antti Kykk\"anen, Joonas Ilmavirta, Maarten V. de Hoop, Pieti Kirkkopelto

arxiv:2606.28527 v1 · 2026-06-26 · math.AG · 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{4URIJ64PYMPOLGC6XXGW7XH6OF}

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	2026-06-30T00:15:16.978991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e52284fb8fc31ee5985ebdcd6fdcfe717b93e89e1277b2d8e2af050d38263cb7

Aliases

arxiv: 2606.28527 · arxiv_version: 2606.28527v1 · doi: 10.48550/arxiv.2606.28527 · pith_short_12: 4URIJ64PYMPO · pith_short_16: 4URIJ64PYMPOLGC6 · pith_short_8: 4URIJ64P

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/4URIJ64PYMPOLGC6XXGW7XH6OF \
  | 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: e52284fb8fc31ee5985ebdcd6fdcfe717b93e89e1277b2d8e2af050d38263cb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4b1ba9b0349cbb5ab3fd9132d91466f737fe8fa8bb5e59b101ca5b68eb3d570",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-06-26T18:22:21Z",
    "title_canon_sha256": "a427035dbb90bb260e2f60b24bc7f7082e23c3d8d7f07987f18ddc399bce19ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28527",
    "kind": "arxiv",
    "version": 1
  }
}