Pith Number

pith:GVZDVMGF

pith:2024:GVZDVMGFKH6MHMQWGGMMROEBP6

not attested not anchored not stored refs pending

Quasilifting of hulls and depth of tensor product of modules

Amit Tripathi, Sutapa Dey

arxiv:2412.01392 v2 · 2024-12-02 · 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{GVZDVMGFKH6MHMQWGGMMROEBP6}

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	2026-07-05T11:59:09.488675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35723ab0c551fcc3b2163198c8b8817faaf309df4636378665fff590fd1e29da

Aliases

arxiv: 2412.01392 · arxiv_version: 2412.01392v2 · doi: 10.48550/arxiv.2412.01392 · pith_short_12: GVZDVMGFKH6M · pith_short_16: GVZDVMGFKH6MHMQW · pith_short_8: GVZDVMGF

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/GVZDVMGFKH6MHMQWGGMMROEBP6 \
  | 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: 35723ab0c551fcc3b2163198c8b8817faaf309df4636378665fff590fd1e29da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c276852f741c9420a9f62e0d47cc8ed02721c7082760a62a5e1ce7bfb492e84",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2024-12-02T11:25:10Z",
    "title_canon_sha256": "7f53d339f3bbd196dc8b1cf1b6ea512721b2779263b7040fd7a87835ecd87e99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.01392",
    "kind": "arxiv",
    "version": 2
  }
}