Pith Number

pith:JMVGIQHW

pith:2016:JMVGIQHWMRZXI7TSMGLNM4PTM3

not attested not anchored not stored refs pending

On the asymptotic linearity of reduction number

Dancheng Lu

arxiv:1608.05769 v3 · 2016-08-20 · 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{JMVGIQHWMRZXI7TSMGLNM4PTM3}

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	2026-05-18T00:35:14.009296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b2a6440f66473747e726196d671f366f31a29c4b9524f42118e210f495854d9

Aliases

arxiv: 1608.05769 · arxiv_version: 1608.05769v3 · doi: 10.48550/arxiv.1608.05769 · pith_short_12: JMVGIQHWMRZX · pith_short_16: JMVGIQHWMRZXI7TS · pith_short_8: JMVGIQHW

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/JMVGIQHWMRZXI7TSMGLNM4PTM3 \
  | 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: 4b2a6440f66473747e726196d671f366f31a29c4b9524f42118e210f495854d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1289303ce993eb944b6793d351ec4674ff9ba3b7903c7c91f21bc8a9f0afa0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-08-20T02:29:21Z",
    "title_canon_sha256": "44eccb94fbeb38ce2a5111f7bd30d646be43a613aa67903ad7b44bb07f5561b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05769",
    "kind": "arxiv",
    "version": 3
  }
}