Pith Number

pith:VQS3ALYQ

pith:2011:VQS3ALYQGIJUIUIGV4EEMSGPPJ

not attested not anchored not stored refs pending

Topological Pressure for sub-additive potentials of amenable group actions

Bingbing Liang, Kesong Yan

arxiv:1104.2195 v2 · 2011-04-12 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VQS3ALYQGIJUIUIGV4EEMSGPPJ}

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	2026-05-18T04:21:51.467516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac25b02f103213445106af084648cf7a63b0db82a63571d9f7db54d4df372fe8

Aliases

arxiv: 1104.2195 · arxiv_version: 1104.2195v2 · doi: 10.48550/arxiv.1104.2195 · pith_short_12: VQS3ALYQGIJU · pith_short_16: VQS3ALYQGIJUIUIG · pith_short_8: VQS3ALYQ

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/VQS3ALYQGIJUIUIGV4EEMSGPPJ \
  | 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: ac25b02f103213445106af084648cf7a63b0db82a63571d9f7db54d4df372fe8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e0c66920bc93d3b6fe9fc31b350aba699c9efc590663e0cb13a1e45816a0618",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-04-12T12:52:53Z",
    "title_canon_sha256": "d0b81eb961edac71ef204afa1b33bdf904682afa4db5029f8a2461517b2213d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2195",
    "kind": "arxiv",
    "version": 2
  }
}