Pith Number

pith:YTILLV5X

pith:2017:YTILLV5XQYIYZPRUZ35HX3W6ZX

not attested not anchored not stored refs pending

The Hilbert series and $a$-invariant of circle invariants

Christopher Seaton, Daniel Herden, Hans-Christian Herbig, L.Emily Cowie

arxiv:1707.03128 v1 · 2017-07-11 · math.RA · math.AC · 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{YTILLV5XQYIYZPRUZ35HX3W6ZX}

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	2026-05-18T00:07:21.965116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4d0b5d7b786118cbe34cefa7beedecdf1efb34137ba6c13d11272a39dd8499f

Aliases

arxiv: 1707.03128 · arxiv_version: 1707.03128v1 · doi: 10.48550/arxiv.1707.03128 · pith_short_12: YTILLV5XQYIY · pith_short_16: YTILLV5XQYIYZPRU · pith_short_8: YTILLV5X

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/YTILLV5XQYIYZPRUZ35HX3W6ZX \
  | 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: c4d0b5d7b786118cbe34cefa7beedecdf1efb34137ba6c13d11272a39dd8499f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16d824d6314d995bde3d7fe2238c2ba84c285b8143797f561f34e46964c728b4",
    "cross_cats_sorted": [
      "math.AC",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2017-07-11T05:00:40Z",
    "title_canon_sha256": "61f7a635bd8fc099bcc0929c6ef1a6ad91be5c0e6fbd1ae2bb395338ace2b0cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.03128",
    "kind": "arxiv",
    "version": 1
  }
}