Pith Number

pith:VPKVK4TY

pith:2016:VPKVK4TYKWZHZLIGLBBFJ5H7LE

not attested not anchored not stored refs pending

Graded Betti numbers of good filtrations

Kamran Lamei, Siamak Yassemi

arxiv:1610.06976 v3 · 2016-10-21 · 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{VPKVK4TYKWZHZLIGLBBFJ5H7LE}

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	2026-05-18T00:23:56.978992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd555727855b27cad06584254f4ff59264bd515ebc27e668ba1a2c3c10f83cb

Aliases

arxiv: 1610.06976 · arxiv_version: 1610.06976v3 · doi: 10.48550/arxiv.1610.06976 · pith_short_12: VPKVK4TYKWZH · pith_short_16: VPKVK4TYKWZHZLIG · pith_short_8: VPKVK4TY

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/VPKVK4TYKWZHZLIGLBBFJ5H7LE \
  | 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: abd555727855b27cad06584254f4ff59264bd515ebc27e668ba1a2c3c10f83cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "009c421f2a44ff35dfd348bff525e72801b8d71994d97ec1eae1f5f80b850dd7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-10-21T23:46:48Z",
    "title_canon_sha256": "4ff84413c96950ce9b6c62367a928c33f0ff7e3675ef63d53cb7abb2f1f6d6eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06976",
    "kind": "arxiv",
    "version": 3
  }
}