Pith Number

pith:MGQGOKTB

pith:2015:MGQGOKTBERDQ54CQB4P5OFVNGG

not attested not anchored not stored refs pending

Complete manifolds with bounded curvature and spectral gaps

Hung Tran, Richard Schoen

arxiv:1510.05046 v2 · 2015-10-16 · math.SP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MGQGOKTBERDQ54CQB4P5OFVNGG}

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	2026-05-18T00:30:49.359645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61a0672a6124470ef0500f1fd716ad31b4ad85af4a51d3b39f585f55083462d0

Aliases

arxiv: 1510.05046 · arxiv_version: 1510.05046v2 · doi: 10.48550/arxiv.1510.05046 · pith_short_12: MGQGOKTBERDQ · pith_short_16: MGQGOKTBERDQ54CQ · pith_short_8: MGQGOKTB

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/MGQGOKTBERDQ54CQB4P5OFVNGG \
  | 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: 61a0672a6124470ef0500f1fd716ad31b4ad85af4a51d3b39f585f55083462d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e4c2cf4d07d73137888aa4a56fe1e000a66e04b88547e17be3c5db4c3975340",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-10-16T23:09:02Z",
    "title_canon_sha256": "c6bd5a705cb690818b6e2d6849cb9610e2c5fa599aa80f53c6a1e7679e286d7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05046",
    "kind": "arxiv",
    "version": 2
  }
}