Pith Number

pith:AUDKK224

pith:2026:AUDKK224PC22IKD2DTWKCHY3OY

not attested not anchored not stored refs pending

The Morse index of constant curvature 2-spheres

Gavin Ball, Jesse Madnick

arxiv:2606.06634 v1 · 2026-06-04 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AUDKK224PC22IKD2DTWKCHY3OY}

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	2026-06-08T01:04:20.151401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0506a56b5c78b5a4287a1ceca11f1b761e2e41ae13cd94f2456b4986bcabed28

Aliases

arxiv: 2606.06634 · arxiv_version: 2606.06634v1 · doi: 10.48550/arxiv.2606.06634 · pith_short_12: AUDKK224PC22 · pith_short_16: AUDKK224PC22IKD2 · pith_short_8: AUDKK224

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/AUDKK224PC22IKD2DTWKCHY3OY \
  | 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: 0506a56b5c78b5a4287a1ceca11f1b761e2e41ae13cd94f2456b4986bcabed28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "068de7dc1d726b8cd591b4f9a93517a30297112bf74553520ab2bc58b55a44d9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-04T18:34:35Z",
    "title_canon_sha256": "07b679df1471f4f247a8131fe7cc63d2de9d43080b65b592bd3c94a58127cecd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06634",
    "kind": "arxiv",
    "version": 1
  }
}