Pith Number

pith:3YB53GHH

pith:2016:3YB53GHHTNHZKIUZOCBOXO4TCH

not attested not anchored not stored refs pending

Approximately fibering a manifold over an aspherical one

Tom Farrell, Wolfgang Lueck, Wolfgang Steimle

arxiv:1603.07934 v3 · 2016-03-25 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3YB53GHHTNHZKIUZOCBOXO4TCH}

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	2026-05-18T00:11:29.087324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de03dd98e79b4f9522997082ebbb9311c76fc632a4a9e22a75f691fd4e7eea30

Aliases

arxiv: 1603.07934 · arxiv_version: 1603.07934v3 · doi: 10.48550/arxiv.1603.07934 · pith_short_12: 3YB53GHHTNHZ · pith_short_16: 3YB53GHHTNHZKIUZ · pith_short_8: 3YB53GHH

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/3YB53GHHTNHZKIUZOCBOXO4TCH \
  | 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: de03dd98e79b4f9522997082ebbb9311c76fc632a4a9e22a75f691fd4e7eea30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c5d465d7cb5702222aa61194c6c8db721f1d295af02fc8d8ebd590a4e780609",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-03-25T15:24:01Z",
    "title_canon_sha256": "58ddd48ab8c13af58bfe16deb3888d5e43a409fabc9cbac0e62a26261fa068e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.07934",
    "kind": "arxiv",
    "version": 3
  }
}