Pith Number

pith:54E5OO7M

pith:2016:54E5OO7MOZ6SWLVYP4QPRIBMF4

not attested not anchored not stored refs pending

Galoisian approach to complex oscillation theory of some Hill equations

Guo-Fu Yu, Yik-Man Chiang

arxiv:1610.09757 v4 · 2016-10-31 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{54E5OO7MOZ6SWLVYP4QPRIBMF4}

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	2026-05-17T23:57:33.109214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef09d73bec767d2b2eb87f20f8a02c2f373046ac4ced8c6aa9be48a252e8777c

Aliases

arxiv: 1610.09757 · arxiv_version: 1610.09757v4 · doi: 10.48550/arxiv.1610.09757 · pith_short_12: 54E5OO7MOZ6S · pith_short_16: 54E5OO7MOZ6SWLVY · pith_short_8: 54E5OO7M

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/54E5OO7MOZ6SWLVYP4QPRIBMF4 \
  | 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: ef09d73bec767d2b2eb87f20f8a02c2f373046ac4ced8c6aa9be48a252e8777c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59781cd4dd9ca0a4c0b921e25474129905c4c6cdbbd9a77bf4a997efdc74290f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-10-31T01:55:30Z",
    "title_canon_sha256": "d4f92d11acd38dcf984f627e37e0f35d2fd5dc845a7a67f56fb558358bce2819"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.09757",
    "kind": "arxiv",
    "version": 4
  }
}