Pith Number

pith:DPS67A2S

pith:2025:DPS67A2SE2D7OPUUXRRUFLFT2N

not attested not anchored not stored refs pending

Smooth functions that split a Klein bottle into two M\"obius bands

Bohdan Mazhar, Sergiy Maksymenko

arxiv:2508.19636 v1 · 2025-08-27 · math.GT · math.AT · 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{DPS67A2SE2D7OPUUXRRUFLFT2N}

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	2026-07-05T12:00:15.572049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1be5ef83522687f73e94bc6342acb3d37f4d211493601be11677316939ed7e28

Aliases

arxiv: 2508.19636 · arxiv_version: 2508.19636v1 · doi: 10.48550/arxiv.2508.19636 · pith_short_12: DPS67A2SE2D7 · pith_short_16: DPS67A2SE2D7OPUU · pith_short_8: DPS67A2S

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/DPS67A2SE2D7OPUUXRRUFLFT2N \
  | 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: 1be5ef83522687f73e94bc6342acb3d37f4d211493601be11677316939ed7e28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72103ef262604e110a6e7e00c76251dd21e22716c38a0185c9acffa17c632177",
    "cross_cats_sorted": [
      "math.AT",
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-08-27T07:25:12Z",
    "title_canon_sha256": "7c0eb4ee2e74cb7f02156c32cfc68fdfc636e3574854d652ec58258671db48c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.19636",
    "kind": "arxiv",
    "version": 1
  }
}