Pith Number

pith:3XB76CLK

pith:2006:3XB76CLKYRX3M46M4MHXU4CUH2

not attested not anchored not stored refs pending

Discreteness and rationality of F-thresholds

Karen E. Smith, Manuel Blickle, Mircea Musta\c{t}\v{a}

arxiv:math/0607660 v2 · 2006-07-26 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XB76CLKYRX3M46M4MHXU4CUH2}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T04:28:28.556225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddc3ff096ac46fb673cce30f7a70543e9504a764c9942d1029225e1173de419f

Aliases

arxiv: math/0607660 · arxiv_version: math/0607660v2 · doi: 10.48550/arxiv.math/0607660 · pith_short_12: 3XB76CLKYRX3 · pith_short_16: 3XB76CLKYRX3M46M · pith_short_8: 3XB76CLK

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/3XB76CLKYRX3M46M4MHXU4CUH2 \
  | 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: ddc3ff096ac46fb673cce30f7a70543e9504a764c9942d1029225e1173de419f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9d284ed3a688bd215dc639726aad81129f9d5dccd586e1ece90861b2f97aaa5",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-07-26T07:00:57Z",
    "title_canon_sha256": "a672ebdde266f3f9130c3c80dd497ca3228b2060a53d6785d7e73d350460f75d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607660",
    "kind": "arxiv",
    "version": 2
  }
}