Pith Number

pith:5OOFUZRL

pith:2016:5OOFUZRLB7NCACQO257BI7TM53

not attested not anchored not stored refs pending

Half dimensional collapse of ends of manifolds of nonpositive curvature

Grigori Avramidi, T. Tam Nguyen Phan

arxiv:1608.02185 v4 · 2016-08-07 · math.GT · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5OOFUZRLB7NCACQO257BI7TM53}

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	2026-05-18T00:12:50.883055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb9c5a662b0fda200a0ed77e147e6ceef76b81ca24927c0aa33dd74c52e0767f

Aliases

arxiv: 1608.02185 · arxiv_version: 1608.02185v4 · doi: 10.48550/arxiv.1608.02185 · pith_short_12: 5OOFUZRLB7NC · pith_short_16: 5OOFUZRLB7NCACQO · pith_short_8: 5OOFUZRL

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/5OOFUZRLB7NCACQO257BI7TM53 \
  | 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: eb9c5a662b0fda200a0ed77e147e6ceef76b81ca24927c0aa33dd74c52e0767f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "197c52888c6a5841aeb52f110532016ba73a65c95d12bf2f070996d3ec58649b",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-08-07T06:03:34Z",
    "title_canon_sha256": "e57ebd952f1d808392725eff62d152298cd8c143b00209fff0d59bbb334dd275"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02185",
    "kind": "arxiv",
    "version": 4
  }
}