Pith Number

pith:UOSXQW3H

pith:2021:UOSXQW3HJTXB2DIWDTR565DEI6

not attested not anchored not stored refs pending

U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology

Chad Giusti, Gregory Henselman-Petrusek, Haibin Hang, Lori Ziegelmeier

arxiv:2108.08831 v2 · 2021-08-19 · math.AT · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UOSXQW3HJTXB2DIWDTR565DEI6}

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	2026-07-05T03:07:31.433225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3a5785b674cee1d0d161ce3df7464479e1b0a1ffe699d8e1870fa6c9603a92c

Aliases

arxiv: 2108.08831 · arxiv_version: 2108.08831v2 · doi: 10.48550/arxiv.2108.08831 · pith_short_12: UOSXQW3HJTXB · pith_short_16: UOSXQW3HJTXB2DIW · pith_short_8: UOSXQW3H

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/UOSXQW3HJTXB2DIWDTR565DEI6 \
  | 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: a3a5785b674cee1d0d161ce3df7464479e1b0a1ffe699d8e1870fa6c9603a92c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b3100e9a379dd12d6c667e6b85b3843e95f88c5fb5ff135dd1542b5c9d359a3",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2021-08-19T17:51:53Z",
    "title_canon_sha256": "8a28380448d625cd969dd182cbd7bc25f07f7aa9f7775d67e78820ef4fcb271d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.08831",
    "kind": "arxiv",
    "version": 2
  }
}