Pith Number

pith:7KWDAKP5

pith:2017:7KWDAKP5IBSJ6TUDHERRVKXPKI

not attested not anchored not stored refs pending

The {\L}ojasiewicz Exponent via The Valuative Hamburger-Noether Process

Szymon Brzostowski, Tomasz Rodak

arxiv:1705.02230 v1 · 2017-05-05 · math.AG · 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{7KWDAKP5IBSJ6TUDHERRVKXPKI}

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	2026-05-18T00:45:00.346420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e

Aliases

arxiv: 1705.02230 · arxiv_version: 1705.02230v1 · doi: 10.48550/arxiv.1705.02230 · pith_short_12: 7KWDAKP5IBSJ · pith_short_16: 7KWDAKP5IBSJ6TUD · pith_short_8: 7KWDAKP5

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/7KWDAKP5IBSJ6TUDHERRVKXPKI \
  | 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: faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05f2139c259156c1b67d960cd44ea95cfda7f121bdff5ee946413fbf97acdb83",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-05-05T13:55:16Z",
    "title_canon_sha256": "bc32b456ec9b43c30f28dcf75ac753b5fba2edf9321c215f42d1f038b3233dd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.02230",
    "kind": "arxiv",
    "version": 1
  }
}