Pith Number

pith:YPQGDPXP

pith:2009:YPQGDPXP4PH7FE66TXD56SND3H

not attested not anchored not stored refs pending

A $K$-theoretical invariant and bifurcation for a parameterized family of functionals

Alessandro Portaluri

arxiv:0905.3897 v2 · 2009-05-24 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YPQGDPXP4PH7FE66TXD56SND3H}

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	2026-05-18T03:17:44.970530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3e061beefe3cff293de9dc7df49a3d9e0d6996efb57d4c5ceddaeaeca7a671d

Aliases

arxiv: 0905.3897 · arxiv_version: 0905.3897v2 · doi: 10.48550/arxiv.0905.3897 · pith_short_12: YPQGDPXP4PH7 · pith_short_16: YPQGDPXP4PH7FE66 · pith_short_8: YPQGDPXP

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/YPQGDPXP4PH7FE66TXD56SND3H \
  | 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: c3e061beefe3cff293de9dc7df49a3d9e0d6996efb57d4c5ceddaeaeca7a671d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "951b159357d28b24081b9b463fddb46c265dd87af541118adf942e3ed0db8bef",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-05-24T12:20:07Z",
    "title_canon_sha256": "4a894eb797df173aff68094a552f90cbafe89f8db79ae8f921b17772d1c3b17d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.3897",
    "kind": "arxiv",
    "version": 2
  }
}