Pith Number

pith:MGBDVLRC

pith:2010:MGBDVLRCEIWV2WB2OXJ5HRYXGV

not attested not anchored not stored refs pending

Torus fibrations and localization of index III

Hajime Fujita, Mikio Furuta, Takahiko Yoshida

arxiv:1008.5007 v3 · 2010-08-30 · math.DG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MGBDVLRCEIWV2WB2OXJ5HRYXGV}

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	2026-05-18T02:47:24.542267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61823aae22222d5d583a75d3d3c717354f93ad71b36f1f2fc165994674c4e035

Aliases

arxiv: 1008.5007 · arxiv_version: 1008.5007v3 · doi: 10.48550/arxiv.1008.5007 · pith_short_12: MGBDVLRCEIWV · pith_short_16: MGBDVLRCEIWV2WB2 · pith_short_8: MGBDVLRC

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/MGBDVLRCEIWV2WB2OXJ5HRYXGV \
  | 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: 61823aae22222d5d583a75d3d3c717354f93ad71b36f1f2fc165994674c4e035

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5b23e34ed37a452a3bfa877e03363b0eef67223733c9b00cdc394aa53031648",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-08-30T05:46:56Z",
    "title_canon_sha256": "0026e96846b00538019fef67eb7be64ec673ecc250d70ec8e07bdaa918c2a707"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.5007",
    "kind": "arxiv",
    "version": 3
  }
}