Pith Number

pith:D3OUJBUN

pith:2021:D3OUJBUNI6MFQOQTNL2N4IVY5L

not attested not anchored not stored refs pending

The Persistent Topology of Optimal Transport Based Metric Thickenings

Facundo M\'emoli, Henry Adams, Michael Moy, Qingsong Wang

arxiv:2109.15061 v3 · 2021-09-30 · math.MG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D3OUJBUNI6MFQOQTNL2N4IVY5L}

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	2026-07-05T08:00:29.757793Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1edd44868d4798583a136af4de22b8eaebc2410ff9df91c11580577de6d4b1a3

Aliases

arxiv: 2109.15061 · arxiv_version: 2109.15061v3 · doi: 10.48550/arxiv.2109.15061 · pith_short_12: D3OUJBUNI6MF · pith_short_16: D3OUJBUNI6MFQOQT · pith_short_8: D3OUJBUN

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/D3OUJBUNI6MFQOQTNL2N4IVY5L \
  | 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: 1edd44868d4798583a136af4de22b8eaebc2410ff9df91c11580577de6d4b1a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dd27505e5b74a963f9c9e440a5f1fdd516fb03cb86ae1eac2b7dd9e691708e4",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2021-09-30T12:19:26Z",
    "title_canon_sha256": "e603935f189c2b1ca334d123f5defaafcded0de6f4812396c015a2ce0ef431a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.15061",
    "kind": "arxiv",
    "version": 3
  }
}