Pith Number

pith:QC4XSVN2

pith:2016:QC4XSVN2A6JFTRU3MJUNSX2KDF

not attested not anchored not stored refs pending

Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets

Diarmuid Crowley, Thomas Schick, Wolfgang Steimle

arxiv:1612.04660 v3 · 2016-12-14 · math.GT · math.AT · 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{QC4XSVN2A6JFTRU3MJUNSX2KDF}

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	2026-05-18T00:00:13.725004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80b97955ba079259c69b6268d95f4a1954c1341401dd4cfab43e61432521e908

Aliases

arxiv: 1612.04660 · arxiv_version: 1612.04660v3 · doi: 10.48550/arxiv.1612.04660 · pith_short_12: QC4XSVN2A6JF · pith_short_16: QC4XSVN2A6JFTRU3 · pith_short_8: QC4XSVN2

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/QC4XSVN2A6JFTRU3MJUNSX2KDF \
  | 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: 80b97955ba079259c69b6268d95f4a1954c1341401dd4cfab43e61432521e908

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23333fb8c74c5da58e98916acc9c7e73ddd1790798055d9976ab6425603ee41b",
    "cross_cats_sorted": [
      "math.AT",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-12-14T14:26:27Z",
    "title_canon_sha256": "287cfa22b5758ff9171ac08838f7f46602e2e52724459fc799130885aa1e94eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04660",
    "kind": "arxiv",
    "version": 3
  }
}