Pith Number

pith:6NPFKRBG

pith:2013:6NPFKRBGYJDE6FFNPTOU7MPLW4

not attested not anchored not stored refs pending

$\mathscr{L}$-invariants and logarithm derivatives of eigenvalues of Frobenius

Yuancao Zhang

arxiv:1307.8245 v1 · 2013-07-31 · 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{6NPFKRBGYJDE6FFNPTOU7MPLW4}

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	2026-05-18T01:48:32.367366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f35e554426c2464f14ad7cdd4fb1ebb7016a0029debc52e0742b7bb14d0b62e4

Aliases

arxiv: 1307.8245 · arxiv_version: 1307.8245v1 · doi: 10.48550/arxiv.1307.8245 · pith_short_12: 6NPFKRBGYJDE · pith_short_16: 6NPFKRBGYJDE6FFN · pith_short_8: 6NPFKRBG

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/6NPFKRBGYJDE6FFNPTOU7MPLW4 \
  | 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: f35e554426c2464f14ad7cdd4fb1ebb7016a0029debc52e0742b7bb14d0b62e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b79eb4ce8d5d2afe6034c9d578b9eb41cb0e72880ac7e4a54a378b9b2ffa8c7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-07-31T08:09:56Z",
    "title_canon_sha256": "cc3f0aa5ea5c0a7994df2fab10a8bc2cfca0cf03daa757f862fe768e5c77cb54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.8245",
    "kind": "arxiv",
    "version": 1
  }
}