Pith Number

pith:4G567R6U

pith:2017:4G567R6U55R75KZDYNV6B4T2YE

not attested not anchored not stored refs pending

Torsion homology growth beyond asymptotics

Oliver Braunling

arxiv:1702.06243 v1 · 2017-02-21 · math.GT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4G567R6U55R75KZDYNV6B4T2YE}

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	2026-05-18T00:50:14.626545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1bbefc7d4ef63feab23c36be0f27ac12fe0a3ca463879698f74d67a90e5768b

Aliases

arxiv: 1702.06243 · arxiv_version: 1702.06243v1 · doi: 10.48550/arxiv.1702.06243 · pith_short_12: 4G567R6U55R7 · pith_short_16: 4G567R6U55R75KZD · pith_short_8: 4G567R6U

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/4G567R6U55R75KZDYNV6B4T2YE \
  | 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: e1bbefc7d4ef63feab23c36be0f27ac12fe0a3ca463879698f74d67a90e5768b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f28eec5a2b4aa4e42615570c53042951011d12167289f85b7a979d81abe0188",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-02-21T02:30:20Z",
    "title_canon_sha256": "5dfc8d6fd7a46720ce4d0cdb77747687ef5fb66728f1b1220e39714e4cdc95a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.06243",
    "kind": "arxiv",
    "version": 1
  }
}