Pith Number

pith:5EBQYYOQ

pith:2015:5EBQYYOQEYGHR62XPRFHSQICMX

not attested not anchored not stored refs pending

Reverse order law for the inverse along an element

Huihui Zhu, Jianlong Chen, Pedro Patricio

arxiv:1512.04875 v2 · 2015-12-15 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5EBQYYOQEYGHR62XPRFHSQICMX}

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	2026-05-18T01:20:03.257450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9030c61d0260c78fb577c4a79410265e7cc60615dff88eb70ecc5661d93ec82

Aliases

arxiv: 1512.04875 · arxiv_version: 1512.04875v2 · doi: 10.48550/arxiv.1512.04875 · pith_short_12: 5EBQYYOQEYGH · pith_short_16: 5EBQYYOQEYGHR62X · pith_short_8: 5EBQYYOQ

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/5EBQYYOQEYGHR62XPRFHSQICMX \
  | 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: e9030c61d0260c78fb577c4a79410265e7cc60615dff88eb70ecc5661d93ec82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd575f0c9267abc5b1307dcaa2850f75891fdb4a3d3ba41a4ab8bd8a39329ed3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-12-15T17:42:16Z",
    "title_canon_sha256": "417da096936cf3b4cb02eaa567faeb8f260b6e7dca50097798d3a8e5a14a73fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04875",
    "kind": "arxiv",
    "version": 2
  }
}