Pith Number

pith:72KPKANA

pith:2018:72KPKANAB6LI7AYDII7ARIMM4S

not attested not anchored not stored refs pending

Tate-Betti and Tate-Bass numbers

Alina Iacob, Edgar Enochs, Sergio Estrada

arxiv:1803.09301 v1 · 2018-03-25 · math.KT · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72KPKANAB6LI7AYDII7ARIMM4S}

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	2026-05-18T00:20:12.068386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe94f501a00f968f8303423e08a18ce49a3a0708c5171f5701d38736e9e4f34c

Aliases

arxiv: 1803.09301 · arxiv_version: 1803.09301v1 · doi: 10.48550/arxiv.1803.09301 · pith_short_12: 72KPKANAB6LI · pith_short_16: 72KPKANAB6LI7AYD · pith_short_8: 72KPKANA

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/72KPKANAB6LI7AYDII7ARIMM4S \
  | 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: fe94f501a00f968f8303423e08a18ce49a3a0708c5171f5701d38736e9e4f34c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7934936e3ad9f40c75e5d2dbace4986144f2d07b04fb5cfe8ae599bb33c4279",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2018-03-25T18:06:57Z",
    "title_canon_sha256": "3019c596b6ad79a5ef7dcfd651663c8f362b9a2196de25f0e59b895dff51895b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.09301",
    "kind": "arxiv",
    "version": 1
  }
}