Pith Number

pith:ZWR7MJCA

pith:2015:ZWR7MJCAZL5Y4BQXFFASGUTNDR

not attested not anchored not stored refs pending

The support of local cohomology modules

Mordechai Katzman, Wenliang Zhang

arxiv:1509.01519 v3 · 2015-09-04 · 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{ZWR7MJCAZL5Y4BQXFFASGUTNDR}

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	2026-05-18T00:45:02.777576Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cda3f62440cafb8e0617294123526d1c528449d4d472562f153faa60340e1685

Aliases

arxiv: 1509.01519 · arxiv_version: 1509.01519v3 · doi: 10.48550/arxiv.1509.01519 · pith_short_12: ZWR7MJCAZL5Y · pith_short_16: ZWR7MJCAZL5Y4BQX · pith_short_8: ZWR7MJCA

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/ZWR7MJCAZL5Y4BQXFFASGUTNDR \
  | 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: cda3f62440cafb8e0617294123526d1c528449d4d472562f153faa60340e1685

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66bd2adbd1389694fb43c23c244460d4ce66490ee58d8dd587348d79d2a5c38b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-09-04T16:16:04Z",
    "title_canon_sha256": "4defc62dd97aeeabd8f87a6c79e7d4849d664c9699b1be1093e902c00979c212"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01519",
    "kind": "arxiv",
    "version": 3
  }
}