Pith Number

pith:3SJTMDXW

pith:2025:3SJTMDXWZVUKUUABPLTMEPDHVQ

not attested not anchored not stored refs pending

Families of Morse functions for manifolds with boundary

Maciej Borodzik, Weronika Buczy\'nska

arxiv:2507.15847 v1 · 2025-07-21 · 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{3SJTMDXWZVUKUUABPLTMEPDHVQ}

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.

Cited by

2 papers in Pith

Reidemeister and movie moves for involutive links

Receipt and verification

First computed	2026-07-05T11:40:45.720935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc93360ef6cd68aa50017ae6c23c67ac25d85fc195e8eb4ba5266b0f2536e33e

Aliases

arxiv: 2507.15847 · arxiv_version: 2507.15847v1 · doi: 10.48550/arxiv.2507.15847 · pith_short_12: 3SJTMDXWZVUK · pith_short_16: 3SJTMDXWZVUKUUAB · pith_short_8: 3SJTMDXW

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/3SJTMDXWZVUKUUABPLTMEPDHVQ \
  | 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: dc93360ef6cd68aa50017ae6c23c67ac25d85fc195e8eb4ba5266b0f2536e33e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8f020688715a1f419097a3dfd36ab4a577000c7e64f9add3b50ad13406e8280",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-07-21T17:55:11Z",
    "title_canon_sha256": "71ccd264107f38d7e518536a4c206539ad474cb26d9466b19bb27933b48c1244"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15847",
    "kind": "arxiv",
    "version": 1
  }
}