Pith Number

pith:QG3AIN5U

pith:2025:QG3AIN5UJN3TL6TWAS5YDAUXKG

not attested not anchored not stored refs pending

Differentiable structures on a union of two open sets

Mykola Lysynskyi, Sergiy Maksymenko

arxiv:2507.05156 v1 · 2025-07-07 · math.DG · math.AG · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QG3AIN5UJN3TL6TWAS5YDAUXKG}

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	2026-07-05T11:33:09.957408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81b60437b44b7735fa7604bb81829751b2627bef3f5cb92560db4107216236af

Aliases

arxiv: 2507.05156 · arxiv_version: 2507.05156v1 · doi: 10.48550/arxiv.2507.05156 · pith_short_12: QG3AIN5UJN3T · pith_short_16: QG3AIN5UJN3TL6TW · pith_short_8: QG3AIN5U

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/QG3AIN5UJN3TL6TWAS5YDAUXKG \
  | 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: 81b60437b44b7735fa7604bb81829751b2627bef3f5cb92560db4107216236af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c987f50f782d01dcd93ef38f0d7b0950909036fbfb719b34bd6e3054c02d8edb",
    "cross_cats_sorted": [
      "math.AG",
      "math.AT",
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-07T16:12:18Z",
    "title_canon_sha256": "bcbfb41404e96cf90d97af9787e6970bceb06e0cdda216b98edf4d8860bdc5e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.05156",
    "kind": "arxiv",
    "version": 1
  }
}