Pith Number

pith:IB5E67TW

pith:2025:IB5E67TW7B56MNJPHJT2HGOOPA

not attested not anchored not stored refs pending

Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes

Mohammad Adarbeh, Mohammad Saleh

arxiv:2509.01638 v3 · 2025-09-01 · 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{IB5E67TW7B56MNJPHJT2HGOOPA}

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	2026-06-09T01:05:09.086614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

407a4f7e76f87be6352f3a67a399ce780b9653466e364ae3fdaf52a5ee6c03ad

Aliases

arxiv: 2509.01638 · arxiv_version: 2509.01638v3 · doi: 10.48550/arxiv.2509.01638 · pith_short_12: IB5E67TW7B56 · pith_short_16: IB5E67TW7B56MNJP · pith_short_8: IB5E67TW

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/IB5E67TW7B56MNJPHJT2HGOOPA \
  | 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: 407a4f7e76f87be6352f3a67a399ce780b9653466e364ae3fdaf52a5ee6c03ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95b5ad1c45337a01c31dcbe02534baebae01b9a0fec7345214e434a8e87f60ff",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2025-09-01T17:32:21Z",
    "title_canon_sha256": "1c6179f41780c0055b350af3bc88b4161536d45dc4e1cd9f5c4b117bf825db8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01638",
    "kind": "arxiv",
    "version": 3
  }
}