Pith Number

pith:I3U3GWXY

pith:2016:I3U3GWXY7Y32ECNNVIFGT2SNRU

not attested not anchored not stored refs pending

Critical metrics of the volume functional on compact three-manifolds with smooth boundary

E. Ribeiro Jr, M. Ranieri, R. Batista, R. Di\'ogenes

arxiv:1603.05456 v2 · 2016-03-17 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I3U3GWXY7Y32ECNNVIFGT2SNRU}

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	2026-05-18T01:12:01.444836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e9b35af8fe37a209adaa0a69ea4d8d161beb3006d5dedd3d7695ac7c48eba5

Aliases

arxiv: 1603.05456 · arxiv_version: 1603.05456v2 · doi: 10.48550/arxiv.1603.05456 · pith_short_12: I3U3GWXY7Y32 · pith_short_16: I3U3GWXY7Y32ECNN · pith_short_8: I3U3GWXY

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/I3U3GWXY7Y32ECNNVIFGT2SNRU \
  | 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: 46e9b35af8fe37a209adaa0a69ea4d8d161beb3006d5dedd3d7695ac7c48eba5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d03d739d146a700be07b81b4e4e6e57c528fce9814ef18d6a314ad1ba0a8ba94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-03-17T12:41:20Z",
    "title_canon_sha256": "7ee6a3d29dfa5d52e92c18450be0721d85ab2fbd34eebd33e7deb3d714a31e2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.05456",
    "kind": "arxiv",
    "version": 2
  }
}