Pith Number

pith:O37IT26I

pith:2016:O37IT26IQINR3WLQWBHKDKEXFH

not attested not anchored not stored refs pending

Spectral gap on Riemannian path space over static and evolving manifolds

Anton Thalmaier, Li-Juan Cheng

arxiv:1611.02165 v1 · 2016-11-07 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O37IT26IQINR3WLQWBHKDKEXFH}

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	2026-05-18T01:00:02.975639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76fe89ebc8821b1dd970b04ea1a89729f74b4f28d51aa3c95969149ff0d2f692

Aliases

arxiv: 1611.02165 · arxiv_version: 1611.02165v1 · doi: 10.48550/arxiv.1611.02165 · pith_short_12: O37IT26IQINR · pith_short_16: O37IT26IQINR3WLQ · pith_short_8: O37IT26I

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/O37IT26IQINR3WLQWBHKDKEXFH \
  | 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: 76fe89ebc8821b1dd970b04ea1a89729f74b4f28d51aa3c95969149ff0d2f692

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07ddd4cdbbee19e814cd604fecd05839538af267df90c946b62443a7cfae1888",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-07T16:43:22Z",
    "title_canon_sha256": "939d872f0fef657ffc764eb441e84c0873dedf9e39cc7ae02e0859d37ef0c412"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.02165",
    "kind": "arxiv",
    "version": 1
  }
}