Pith Number

pith:BIWNMQQT

pith:2007:BIWNMQQTN4F3TBK2R3WT5YQCXD

not attested not anchored not stored refs pending

Tame kernels and further 4-rank densites

Brian Murray, Robert Osburn

arxiv:math/0703324 v1 · 2007-03-12 · math.NT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BIWNMQQTN4F3TBK2R3WT5YQCXD}

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	2026-07-05T02:11:32.872727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a2cd642136f0bb9855a8eed3ee202b8ea008742b99267efa39752b59a07eac2

Aliases

arxiv: math/0703324 · arxiv_version: math/0703324v1 · doi: 10.48550/arxiv.math/0703324 · pith_short_12: BIWNMQQTN4F3 · pith_short_16: BIWNMQQTN4F3TBK2 · pith_short_8: BIWNMQQT

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/BIWNMQQTN4F3TBK2R3WT5YQCXD \
  | 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: 0a2cd642136f0bb9855a8eed3ee202b8ea008742b99267efa39752b59a07eac2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fdc5bb6a089478338c53ae3325b13e805661e62a5053eb1adf443dd030d138b",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-03-12T09:13:19Z",
    "title_canon_sha256": "a69c59ebc2d2c4db2c90421519cb4cdce09a0db625d205cfdd2628d229c43d95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703324",
    "kind": "arxiv",
    "version": 1
  }
}