Pith Number

pith:ZULG3HJ5

pith:2009:ZULG3HJ5DL5HUKQKPA3575IUYI

not attested not anchored not stored refs pending

Gross-Hopkins duality and the Gorenstein condition

J. P. C. Greenlees, S. B. Iyengar, W. G. Dwyer

arxiv:0905.4777 v2 · 2009-05-29 · math.AT · 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{ZULG3HJ5DL5HUKQKPA3575IUYI}

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	2026-05-18T04:41:44.107560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd166d9d3d1afa7a2a0a7837dff514c2015debf0fb27968725399b04b477448b

Aliases

arxiv: 0905.4777 · arxiv_version: 0905.4777v2 · doi: 10.48550/arxiv.0905.4777 · pith_short_12: ZULG3HJ5DL5H · pith_short_16: ZULG3HJ5DL5HUKQK · pith_short_8: ZULG3HJ5

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/ZULG3HJ5DL5HUKQKPA3575IUYI \
  | 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: cd166d9d3d1afa7a2a0a7837dff514c2015debf0fb27968725399b04b477448b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4f0e22208a0fc04cf40cc674896b4d7622a5b84d6385e19f86c75465d5075f4",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-05-29T02:44:37Z",
    "title_canon_sha256": "1834c89c05c7830ef5e796af8de76398c68e534b9eb044e5aa8e79897775a745"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.4777",
    "kind": "arxiv",
    "version": 2
  }
}