Pith Number

pith:GBEB3NQG

pith:2009:GBEB3NQGQDJ5UCW35K5Y3TI74N

not attested not anchored not stored refs pending

Perturbation of a warped product metric of an end and the growth property of solutions to eigenvalue equation

Hironori Kumura

arxiv:0907.4038 v2 · 2009-07-23 · math.DG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GBEB3NQGQDJ5UCW35K5Y3TI74N}

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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	2026-05-18T02:29:30.384582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30481db60680d3da0adbeabb8dcd1fe37f37ca43fa8b6ef6f09e8e8c5357a1cd

Aliases

arxiv: 0907.4038 · arxiv_version: 0907.4038v2 · doi: 10.48550/arxiv.0907.4038 · pith_short_12: GBEB3NQGQDJ5 · pith_short_16: GBEB3NQGQDJ5UCW3 · pith_short_8: GBEB3NQG

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/GBEB3NQGQDJ5UCW35K5Y3TI74N \
  | 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: 30481db60680d3da0adbeabb8dcd1fe37f37ca43fa8b6ef6f09e8e8c5357a1cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48f92778eeeb2c10421f9e91b20fa5511d0cdd5322c8b03aeef1e284f94ef6e3",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-07-23T12:02:40Z",
    "title_canon_sha256": "26e942c9b1b34537ce2c2ca493044853222658493dc99153820cc1f1a708c465"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4038",
    "kind": "arxiv",
    "version": 2
  }
}