Pith Number

pith:JOTDCLE5

pith:2007:JOTDCLE5LNVW6UDZJ64RGYPB5L

not attested not anchored not stored refs pending

Structure and finiteness properties of subdirect products of groups

Charles F Miller III, Martin R Bridson

arxiv:0708.4331 v1 · 2007-08-31 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JOTDCLE5LNVW6UDZJ64RGYPB5L}

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	2026-05-18T02:58:12.395790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ba6312c9d5b6b6f50794fb91361e1ead1bd950eb6a157102c093004623473ac

Aliases

arxiv: 0708.4331 · arxiv_version: 0708.4331v1 · doi: 10.48550/arxiv.0708.4331 · pith_short_12: JOTDCLE5LNVW · pith_short_16: JOTDCLE5LNVW6UDZ · pith_short_8: JOTDCLE5

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/JOTDCLE5LNVW6UDZJ64RGYPB5L \
  | 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: 4ba6312c9d5b6b6f50794fb91361e1ead1bd950eb6a157102c093004623473ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3936be40b5d8c7fba99e85396f604d6dbdde690c0e234065f160a64b8c18faff",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2007-08-31T12:30:46Z",
    "title_canon_sha256": "3eb20c07320a00d03686323b4d855aa25ff91eb61583e212681d15b3e748a68e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.4331",
    "kind": "arxiv",
    "version": 1
  }
}