Pith Number

pith:7RIO7CI6

pith:2015:7RIO7CI6F3IDC4DNLBIYQCGQSK

not attested not anchored not stored refs pending

Ascent and descent of the Golod property along algebra retracts

Anjan Gupta

arxiv:1511.09292 v2 · 2015-11-30 · 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{7RIO7CI6F3IDC4DNLBIYQCGQSK}

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	2026-05-18T00:38:31.483541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc50ef891e2ed031706d58518808d0929c482ad663c67598bcc8ab3c6512e6ba

Aliases

arxiv: 1511.09292 · arxiv_version: 1511.09292v2 · doi: 10.48550/arxiv.1511.09292 · pith_short_12: 7RIO7CI6F3ID · pith_short_16: 7RIO7CI6F3IDC4DN · pith_short_8: 7RIO7CI6

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/7RIO7CI6F3IDC4DNLBIYQCGQSK \
  | 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: fc50ef891e2ed031706d58518808d0929c482ad663c67598bcc8ab3c6512e6ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f934875d10e03aa66df30b32ef8506f5c52d939a62395773e0ce19300ac3b6f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-11-30T13:11:12Z",
    "title_canon_sha256": "509fd088a28634f906ea4e5fce33930b78890d53a1d99c96a31667dcfd5b6474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09292",
    "kind": "arxiv",
    "version": 2
  }
}