Pith Number

pith:4H24JHFR

pith:2017:4H24JHFRBZ5PB4FEXNBS4IFKP6

not attested not anchored not stored refs pending

Interpolating Between Hilbert-Samuel and Hilbert-Kunz Multiplicity

William D. Taylor

arxiv:1706.07445 v1 · 2017-06-22 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4H24JHFRBZ5PB4FEXNBS4IFKP6}

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	2026-05-18T00:41:49.045115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1f5c49cb10e7af0f0a4bb432e20aa7f9a311a24b476d17d3c631666db8cba37

Aliases

arxiv: 1706.07445 · arxiv_version: 1706.07445v1 · doi: 10.48550/arxiv.1706.07445 · pith_short_12: 4H24JHFRBZ5P · pith_short_16: 4H24JHFRBZ5PB4FE · pith_short_8: 4H24JHFR

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/4H24JHFRBZ5PB4FEXNBS4IFKP6 \
  | 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: e1f5c49cb10e7af0f0a4bb432e20aa7f9a311a24b476d17d3c631666db8cba37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "406bf843ee95c3d5343d96a9f75e9d8eca9808968260353d38c3a0d447b0f422",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-06-22T18:09:06Z",
    "title_canon_sha256": "5ca572bbe1fae2b51f8073c4b2e529f3316d1ba44754e362ebb5671205341910"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.07445",
    "kind": "arxiv",
    "version": 1
  }
}