Pith Number

pith:XXIY5Z5K

pith:2026:XXIY5Z5K7HQGFCWLR6GPL2KP6O

not attested not anchored not stored refs pending

Milnor metric for Morse--Smale flows from field theory

Giovanni Molinari, Michele Schiavina

arxiv:2607.24238 v1 · 2026-07-27 · math-ph · math.AT · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XXIY5Z5K7HQGFCWLR6GPL2KP6O}

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	2026-07-28T02:23:52.789306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5

Aliases

arxiv: 2607.24238 · arxiv_version: 2607.24238v1 · doi: 10.48550/arxiv.2607.24238 · pith_short_12: XXIY5Z5K7HQG · pith_short_16: XXIY5Z5K7HQGFCWL · pith_short_8: XXIY5Z5K

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/XXIY5Z5K7HQGFCWLR6GPL2KP6O \
  | 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: bdd18ee7aaf9e0628acb8f8cf5e94ff3b485c00f551dbd4a60a25c1bcba11dd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed948f93f73ff78567eb04235e1ec964477b894fd9539743ef7f291f753be00e",
    "cross_cats_sorted": [
      "math.AT",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-27T10:17:20Z",
    "title_canon_sha256": "26a0bdeb1e8c03d2e4d06bb5aeb52a706d5b3eb35ad8cccc17327f8f45da015a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24238",
    "kind": "arxiv",
    "version": 1
  }
}