Pith Number

pith:GVNXYLBX

pith:2015:GVNXYLBX466SR5JCN5M6R6WEAR

not attested not anchored not stored refs pending

The $\mathcal{L}$-invariant, the dual $\mathcal{L}$-invariant, and families

Jonathan Pottharst

arxiv:1512.00930 v1 · 2015-12-03 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GVNXYLBX466SR5JCN5M6R6WEAR}

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	2026-05-18T01:25:23.807784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

355b7c2c37e7bd28f5226f59e8fac40475a54063e362e503fdcb31d17b6fc4d4

Aliases

arxiv: 1512.00930 · arxiv_version: 1512.00930v1 · doi: 10.48550/arxiv.1512.00930 · pith_short_12: GVNXYLBX466S · pith_short_16: GVNXYLBX466SR5JC · pith_short_8: GVNXYLBX

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/GVNXYLBX466SR5JCN5M6R6WEAR \
  | 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: 355b7c2c37e7bd28f5226f59e8fac40475a54063e362e503fdcb31d17b6fc4d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aef2aba0215efd728f0f9aa69d935a598c522981831799999d61caf85d29188e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-03T02:45:19Z",
    "title_canon_sha256": "65cec3f52fd4d106f4566b72cd325c00e10db7f7ed58401c2d36213fe9e69144"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00930",
    "kind": "arxiv",
    "version": 1
  }
}