Pith Number

pith:LVCYBPVG

pith:2016:LVCYBPVGMTNFG6WZOVXYMK6X6B

not attested not anchored not stored refs pending

$D$-module and $F$-module length of local cohomology modules

Ilya Smirnov, Linquan Ma, Mordechai Katzman, Wenliang Zhang

arxiv:1609.01643 v3 · 2016-09-06 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LVCYBPVGMTNFG6WZOVXYMK6X6B}

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	2026-05-18T00:44:57.765358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d4580bea664da537ad9756f862bd7f0565e1f5411dc2f9d20c948e4bf27a497

Aliases

arxiv: 1609.01643 · arxiv_version: 1609.01643v3 · doi: 10.48550/arxiv.1609.01643 · pith_short_12: LVCYBPVGMTNF · pith_short_16: LVCYBPVGMTNFG6WZ · pith_short_8: LVCYBPVG

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/LVCYBPVGMTNFG6WZOVXYMK6X6B \
  | 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: 5d4580bea664da537ad9756f862bd7f0565e1f5411dc2f9d20c948e4bf27a497

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af9f0421023fd04f970ccd1cce4666b9e5cdc74327f0f2e7da24364f518a31cd",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-09-06T16:32:32Z",
    "title_canon_sha256": "ca92d9f6f422a322d1a85519ead7a5a137c94d62cec1ad486e35c685d6785257"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01643",
    "kind": "arxiv",
    "version": 3
  }
}