Pith Number

pith:UVAUNK45

pith:2016:UVAUNK45D77RX74VPMNOKCATGN

not attested not anchored not stored refs pending

Homology and homotopy complexity in negative curvature

Roman Sauer, Tsachik Gelander, Uri Bader

arxiv:1612.04871 v5 · 2016-12-14 · math.GT · 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{UVAUNK45D77RX74VPMNOKCATGN}

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	2026-05-18T00:04:08.497801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a54146ab9d1fff1bff957b1ae5081333797d804352261c3704e05ca0806f55bf

Aliases

arxiv: 1612.04871 · arxiv_version: 1612.04871v5 · doi: 10.48550/arxiv.1612.04871 · pith_short_12: UVAUNK45D77R · pith_short_16: UVAUNK45D77RX74V · pith_short_8: UVAUNK45

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/UVAUNK45D77RX74VPMNOKCATGN \
  | 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: a54146ab9d1fff1bff957b1ae5081333797d804352261c3704e05ca0806f55bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "311205c4782a1ab4492b7b6d35430db5a92ea0d7e2360170284cf05706e75112",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-12-14T22:37:05Z",
    "title_canon_sha256": "4b912255a3bd8283427024a133d86715100e0ddd252403541200541bb59a2d39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04871",
    "kind": "arxiv",
    "version": 5
  }
}