Pith Number

pith:HKOEUG7R

pith:2018:HKOEUG7RQAEULUUFERCTBBYT4A

not attested not anchored not stored refs pending

Nonorientable, incompressible surfaces in punctured-torus bundles over S^1

Jozef H. Przytycki

arxiv:1812.11228 v1 · 2018-12-28 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HKOEUG7RQAEULUUFERCTBBYT4A}

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	2026-05-17T23:57:12.500562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a9c4a1bf1800945d2852445308713e01d788d0645c3c4c73cb0efd82a021443

Aliases

arxiv: 1812.11228 · arxiv_version: 1812.11228v1 · doi: 10.48550/arxiv.1812.11228 · pith_short_12: HKOEUG7RQAEU · pith_short_16: HKOEUG7RQAEULUUF · pith_short_8: HKOEUG7R

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/HKOEUG7RQAEULUUFERCTBBYT4A \
  | 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: 3a9c4a1bf1800945d2852445308713e01d788d0645c3c4c73cb0efd82a021443

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "674c2f9ebca1cf6393e9b5bd6f274d70cdd144ae301ed4f6213369e55cced1c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-12-28T21:53:09Z",
    "title_canon_sha256": "7a5da271f093674b7cb801b4b29192b2405c8cd6e52894a3059c58904bb4607c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.11228",
    "kind": "arxiv",
    "version": 1
  }
}