Pith Number

pith:3N2GUMJR

pith:2024:3N2GUMJRMANJS7H5WDHTV5KNOY

not attested not anchored not stored refs pending

Immersed but not embedded homology classes

Diarmuid Crowley, Mark Grant

arxiv:2412.15359 v2 · 2024-12-19 · 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{3N2GUMJRMANJS7H5WDHTV5KNOY}

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	2026-07-05T10:02:56.462056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db746a3131601a997cfdb0cf3af54d7601b995248261c27edc24f6de5e777413

Aliases

arxiv: 2412.15359 · arxiv_version: 2412.15359v2 · doi: 10.48550/arxiv.2412.15359 · pith_short_12: 3N2GUMJRMANJ · pith_short_16: 3N2GUMJRMANJS7H5 · pith_short_8: 3N2GUMJR

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/3N2GUMJRMANJS7H5WDHTV5KNOY \
  | 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: db746a3131601a997cfdb0cf3af54d7601b995248261c27edc24f6de5e777413

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5df0d92c685b5fd176fb5cb2cc4911c40d332557240ea62a5745425ca7307ca5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-12-19T19:45:34Z",
    "title_canon_sha256": "2566e531b32a56055ae8fb4f693579b0bf64c1b1d56c1ba3852375bc4244dbd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.15359",
    "kind": "arxiv",
    "version": 2
  }
}