Pith Number

pith:L5G5OR3V

pith:2016:L5G5OR3VI7XBPMYOGFCAZCJSMS

not attested not anchored not stored refs pending

Shift equivalence in the generalized factor order

Brian Miceli, Daniel Glasscock, Jay Pantone, Jennifer Fidler, Min Xu

arxiv:1612.09003 v1 · 2016-12-28 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5G5OR3VI7XBPMYOGFCAZCJSMS}

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	2026-05-18T00:53:46.666452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f4dd7477547ee17b30e31440c893264a79597e9aa7f8c90a1dc0d59ff16ff9f

Aliases

arxiv: 1612.09003 · arxiv_version: 1612.09003v1 · doi: 10.48550/arxiv.1612.09003 · pith_short_12: L5G5OR3VI7XB · pith_short_16: L5G5OR3VI7XBPMYO · pith_short_8: L5G5OR3V

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/L5G5OR3VI7XBPMYOGFCAZCJSMS \
  | 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: 5f4dd7477547ee17b30e31440c893264a79597e9aa7f8c90a1dc0d59ff16ff9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73a14087bb0573c690a3548e88a141d978219eaf6cc6a0ddc114e380959ced15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-28T23:09:55Z",
    "title_canon_sha256": "d51948d7d7c1faa1707430534698c4727b6f88835a23e685b4f6c0ff9e52dc47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09003",
    "kind": "arxiv",
    "version": 1
  }
}