Pith Number

pith:HGFJ67S2

pith:2025:HGFJ67S2EUAA3EOUNTU6SWBBWM

not attested not anchored not stored refs pending

Planar $W^{1,\,1}$-extension domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

arxiv:2512.09167 v2 · 2025-12-09 · math.FA · 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{HGFJ67S2EUAA3EOUNTU6SWBBWM}

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	2026-06-02T02:04:12.121014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

398a9f7e5a25000d91d46ce9e95821b3176f6e38b7f254438224d5c91398e3dc

Aliases

arxiv: 2512.09167 · arxiv_version: 2512.09167v2 · doi: 10.48550/arxiv.2512.09167 · pith_short_12: HGFJ67S2EUAA · pith_short_16: HGFJ67S2EUAA3EOU · pith_short_8: HGFJ67S2

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/HGFJ67S2EUAA3EOUNTU6SWBBWM \
  | 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: 398a9f7e5a25000d91d46ce9e95821b3176f6e38b7f254438224d5c91398e3dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c81b8574f6692373d8bd9139275809765b08e3b039c0281ea35d13b5d62dbca1",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-12-09T22:28:21Z",
    "title_canon_sha256": "09889e6c0fd0c76c7efdd4660cf65eb21b8dfad0ff93e697bc2324e65e8fa260"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.09167",
    "kind": "arxiv",
    "version": 2
  }
}