Pith Number

pith:ARHT5EZ6

pith:2014:ARHT5EZ63YDZFSXLBDPZVNQV3G

not attested not anchored not stored refs pending

Involutions on sapphire Sol 3-manifolds and the Borsuk-Ulam theorem for maps into $R^n$

Alexandre Paiva Barreto, Daciberg Lima Gon\c{c}alves, Daniel Vendr\'uscolo

arxiv:1410.0142 v3 · 2014-10-01 · 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{ARHT5EZ63YDZFSXLBDPZVNQV3G}

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	2026-05-18T02:37:44.248303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

044f3e933ede0792caeb08df9ab615d9b8671481155d91fa58b360a84ef2e7aa

Aliases

arxiv: 1410.0142 · arxiv_version: 1410.0142v3 · doi: 10.48550/arxiv.1410.0142 · pith_short_12: ARHT5EZ63YDZ · pith_short_16: ARHT5EZ63YDZFSXL · pith_short_8: ARHT5EZ6

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/ARHT5EZ63YDZFSXLBDPZVNQV3G \
  | 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: 044f3e933ede0792caeb08df9ab615d9b8671481155d91fa58b360a84ef2e7aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8a31f966be99503eb73e247fc62be16579c812023b8378fa5bfcdf65bc9fea0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2014-10-01T08:15:22Z",
    "title_canon_sha256": "ad7465725ca8c75451e137e897b9c3f837992ba766718f03e22e82c1f40c8827"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.0142",
    "kind": "arxiv",
    "version": 3
  }
}