Pith Number

pith:DFHL6DHO

pith:2026:DFHL6DHO6ER4RMEPNVKUBWNTKF

not attested not anchored not stored refs pending

Exceptional rational functions of degree 5 over finite fields: classification by monodromy, ramification, and the Riemann-Hurwitz formula

Xiang Fan, Zhichao Tang

arxiv:2607.05075 v1 · 2026-07-06 · 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{DFHL6DHO6ER4RMEPNVKUBWNTKF}

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	2026-07-07T03:19:15.274694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

194ebf0ceef123c8b08f6d5540d9b3514dc921d7f15612788df1067c776a8b34

Aliases

arxiv: 2607.05075 · arxiv_version: 2607.05075v1 · doi: 10.48550/arxiv.2607.05075 · pith_short_12: DFHL6DHO6ER4 · pith_short_16: DFHL6DHO6ER4RMEP · pith_short_8: DFHL6DHO

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/DFHL6DHO6ER4RMEPNVKUBWNTKF \
  | 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: 194ebf0ceef123c8b08f6d5540d9b3514dc921d7f15612788df1067c776a8b34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b8177bccae386ddd9170a89771730547e4887a6eabde9276f855a9f6189efbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-06T13:37:42Z",
    "title_canon_sha256": "bd66d1efb7e76c01723bb6f091af7bcf6c82e48e16022cfab886d9eeb1039906"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05075",
    "kind": "arxiv",
    "version": 1
  }
}