Pith Number

pith:VOSM3ZL3

pith:2021:VOSM3ZL3MQCK6HLUQCZQZJY3RQ

not attested not anchored not stored refs pending

Volume growth for infinite graphs and translation surfaces

Mark Pollicott, Paul Colognese

arxiv:2107.14078 v2 · 2021-07-29 · 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{VOSM3ZL3MQCK6HLUQCZQZJY3RQ}

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	2026-07-05T03:01:57.869742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aba4cde57b6404af1d7480b30ca71b8c19735d95fbaa1395dac84a9a75c6cc1b

Aliases

arxiv: 2107.14078 · arxiv_version: 2107.14078v2 · doi: 10.48550/arxiv.2107.14078 · pith_short_12: VOSM3ZL3MQCK · pith_short_16: VOSM3ZL3MQCK6HLU · pith_short_8: VOSM3ZL3

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/VOSM3ZL3MQCK6HLUQCZQZJY3RQ \
  | 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: aba4cde57b6404af1d7480b30ca71b8c19735d95fbaa1395dac84a9a75c6cc1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3f344e6669e3ff17cd0317962ac1ff03e75d411998d7394b7896ae2e2c78696",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-07-29T15:09:10Z",
    "title_canon_sha256": "214f796e4e133b3aff8fc85bb39e26c9cad85aacb3004cb3840c2456c3989499"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.14078",
    "kind": "arxiv",
    "version": 2
  }
}