Pith Number

pith:WDCUWWDY

pith:2016:WDCUWWDYGLRVDS6NXY6SZTMJ56

not attested not anchored not stored refs pending

Extremal Betti numbers of graded modules

Marilena Crupi

arxiv:1603.00011 v3 · 2016-02-29 · math.AC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WDCUWWDYGLRVDS6NXY6SZTMJ56}

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	2026-05-18T01:11:17.555126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0c54b587832e351cbcdbe3d2ccd89efb43b4169aad1ca2bd0560434a1aadd70

Aliases

arxiv: 1603.00011 · arxiv_version: 1603.00011v3 · doi: 10.48550/arxiv.1603.00011 · pith_short_12: WDCUWWDYGLRV · pith_short_16: WDCUWWDYGLRVDS6N · pith_short_8: WDCUWWDY

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/WDCUWWDYGLRVDS6NXY6SZTMJ56 \
  | 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: b0c54b587832e351cbcdbe3d2ccd89efb43b4169aad1ca2bd0560434a1aadd70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a6d0a793e9bd87abed0f625df439dd76d2cce5748a6192ee5a8261a34c2aacf",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-02-29T08:47:27Z",
    "title_canon_sha256": "beb738b19d05bd24bbb0b3194296a06e2d358cd141626a623deccbcf82fdd844"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00011",
    "kind": "arxiv",
    "version": 3
  }
}