Pith Number

pith:3E7K47AS

pith:2015:3E7K47ASH4XREDDHAZSSHBBRET

not attested not anchored not stored refs pending

On $L_{n}$-Injective Modules and $L_{n}$-Injective Dimensions

Fanggui Wang, Lei Qiao, Qing Li, Shiqi Xing, Tao Xiong

arxiv:1509.07235 v1 · 2015-09-24 · math.RA · 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{3E7K47ASH4XREDDHAZSSHBBRET}

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	2026-05-18T01:32:09.477015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d93eae7c123f2f120c67066523843124e3bc5aff0182a6202db024b3832a2d79

Aliases

arxiv: 1509.07235 · arxiv_version: 1509.07235v1 · doi: 10.48550/arxiv.1509.07235 · pith_short_12: 3E7K47ASH4XR · pith_short_16: 3E7K47ASH4XREDDH · pith_short_8: 3E7K47AS

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/3E7K47ASH4XREDDHAZSSHBBRET \
  | 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: d93eae7c123f2f120c67066523843124e3bc5aff0182a6202db024b3832a2d79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d201ecc7a805ab7ca89a27ad1c8fc460ad079fb0e7e9194f21afb8df65023ef7",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-09-24T05:05:18Z",
    "title_canon_sha256": "9031fb421cc2a2fe432959e6551a640c95b49b21c1c899a0ed06c4ccbe3b25d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07235",
    "kind": "arxiv",
    "version": 1
  }
}