Pith Number

pith:MXY2EDQU

pith:2013:MXY2EDQUR7MKU7CS2VXL5WTBNK

not attested not anchored not stored refs pending

Discrete Morse Theory and a Reformulation of the K(\pi,1)-conjecture

Viktoriya Ozornova

arxiv:1309.1337 v2 · 2013-09-05 · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MXY2EDQUR7MKU7CS2VXL5WTBNK}

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	2026-05-18T03:13:12.308763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65f1a20e148fd8aa7c52d56ebeda616ab49768da3b6983706b01d7ef913658e1

Aliases

arxiv: 1309.1337 · arxiv_version: 1309.1337v2 · doi: 10.48550/arxiv.1309.1337 · pith_short_12: MXY2EDQUR7MK · pith_short_16: MXY2EDQUR7MKU7CS · pith_short_8: MXY2EDQU

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/MXY2EDQUR7MKU7CS2VXL5WTBNK \
  | 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: 65f1a20e148fd8aa7c52d56ebeda616ab49768da3b6983706b01d7ef913658e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9cfbca0a452ffd6a277e1ad7c5246058b23755243b0fb6c82021025547bfb4e0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2013-09-05T12:50:14Z",
    "title_canon_sha256": "9381cb693c488b1f500dd1313d976baaf84e9274125745475c44a66d7b9cc5cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1337",
    "kind": "arxiv",
    "version": 2
  }
}