Pith Number

pith:6GSGAPV6

pith:2009:6GSGAPV6747EK72AXFWEURL3YE

not attested not anchored not stored refs pending

hbar-expansion of KP hierarchy: Recursive construction of solutions

Kanehisa Takasaki, Takashi Takebe

arxiv:0912.4867 v2 · 2009-12-24 · math-ph · hep-th · math.MP · math.QA · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6GSGAPV6747EK72AXFWEURL3YE}

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	2026-05-18T04:41:16.331380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1a4603ebeff3e457f40b96c4a457bc109f623fcfde41a5f9548e797b3c77586

Aliases

arxiv: 0912.4867 · arxiv_version: 0912.4867v2 · doi: 10.48550/arxiv.0912.4867 · pith_short_12: 6GSGAPV6747E · pith_short_16: 6GSGAPV6747EK72A · pith_short_8: 6GSGAPV6

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/6GSGAPV6747EK72AXFWEURL3YE \
  | 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: f1a4603ebeff3e457f40b96c4a457bc109f623fcfde41a5f9548e797b3c77586

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4c227897d52f683c5e76eb6529f5ba1197134362b105e14816386327ffa0896",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "math.QA",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-12-24T14:17:15Z",
    "title_canon_sha256": "0afca9c9ac8869729817fc02c573611f14c89f7f3cdae0c89a9ff3175ff12452"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4867",
    "kind": "arxiv",
    "version": 2
  }
}