Pith Number

pith:7VGK7BGL

pith:2012:7VGK7BGLLNSL3YL3K7DOK6PMC5

not attested not anchored not stored refs pending

N-step energy of maps and fixed-point property of random groups

Hiroyasu Izeki, Shin Nayatani, Takefumi Kondo

arxiv:1210.5829 v1 · 2012-10-22 · math.DG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7VGK7BGLLNSL3YL3K7DOK6PMC5}

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	2026-05-18T03:42:35.013809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd4caf84cb5b64bde17b57c6e579ec17424a808d0169a549767d09aa9a73ae41

Aliases

arxiv: 1210.5829 · arxiv_version: 1210.5829v1 · doi: 10.48550/arxiv.1210.5829 · pith_short_12: 7VGK7BGLLNSL · pith_short_16: 7VGK7BGLLNSL3YL3 · pith_short_8: 7VGK7BGL

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/7VGK7BGLLNSL3YL3K7DOK6PMC5 \
  | 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: fd4caf84cb5b64bde17b57c6e579ec17424a808d0169a549767d09aa9a73ae41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74655d7dcdfb4d32aa62f7193d4f3a35ee3228965995e7b60ec4dc74608ecf6e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-10-22T08:18:23Z",
    "title_canon_sha256": "c847abdbd6786cc3d22535ff8f25159f6da725337ee13f2e8def686eb83d5e02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5829",
    "kind": "arxiv",
    "version": 1
  }
}