Pith Number

pith:DPNELFMX

pith:2025:DPNELFMXUYC5UWGKQ456JENL5Q

not attested not anchored not stored refs pending

Milnor invariants and thickness of spherical links

Fedor Manin, Rafa{\l} Komendarczyk, Robin Koytcheff

arxiv:2509.02883 v1 · 2025-09-02 · math.GT · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DPNELFMXUYC5UWGKQ456JENL5Q}

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	2026-07-05T12:03:59.196255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bda459597a605da58ca873be491abec23787b3cd106a0180dadd348d2e97c35

Aliases

arxiv: 2509.02883 · arxiv_version: 2509.02883v1 · doi: 10.48550/arxiv.2509.02883 · pith_short_12: DPNELFMXUYC5 · pith_short_16: DPNELFMXUYC5UWGK · pith_short_8: DPNELFMX

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/DPNELFMXUYC5UWGKQ456JENL5Q \
  | 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: 1bda459597a605da58ca873be491abec23787b3cd106a0180dadd348d2e97c35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "600facbd57f2feab36218f85c6f47a6ad9ffb3e6b77faff836b470be6abd3c40",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-09-02T23:06:07Z",
    "title_canon_sha256": "f080e39434944ba6a0c5603055962e58c648f844018b4b24b5c041bfb6380058"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.02883",
    "kind": "arxiv",
    "version": 1
  }
}