Pith Number

pith:OIFGHDL4

pith:2026:OIFGHDL4CWCYQIHSMKKH6SQFYJ

not attested not anchored not stored refs pending

Morse complexity of homology classes

Bena Tshishiku, Fedor Manin, Shmuel Weinberger

arxiv:2607.20259 v1 · 2026-07-22 · 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{OIFGHDL4CWCYQIHSMKKH6SQFYJ}

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	2026-07-23T01:25:10.524687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

720a638d7c15858820f262947f4a05c26082a3ceaaad0897f91bad8a4d3749a6

Aliases

arxiv: 2607.20259 · arxiv_version: 2607.20259v1 · doi: 10.48550/arxiv.2607.20259 · pith_short_12: OIFGHDL4CWCY · pith_short_16: OIFGHDL4CWCYQIHS · pith_short_8: OIFGHDL4

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/OIFGHDL4CWCYQIHSMKKH6SQFYJ \
  | 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: 720a638d7c15858820f262947f4a05c26082a3ceaaad0897f91bad8a4d3749a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9689e313b5a711a8c2895f44099a4601e3391d9526d9dae93556ec945f5cded",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-22T15:15:50Z",
    "title_canon_sha256": "3372d3646df9d03c1dcf8917594b95bb050be8ae97feea46181dad61c5d73137"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20259",
    "kind": "arxiv",
    "version": 1
  }
}