Pith Number

pith:Z2GXCAU2

pith:2026:Z2GXCAU2O6QIVPUMWQDANZGIWB

not attested not anchored not stored refs resolved

Distance-Preserving Digests: A Primitive for BFT Consensus

Ryan Patrick Mercier

Replacing collision-resistant hashes with 8D vector-sum digests lets BFT protocols measure agreement early and use smaller committees while keeping safety.

arxiv:2605.15329 v1 · 2026-05-14 · cs.CR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z2GXCAU2O6QIVPUMWQDANZGIWB}

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.

Claims

C1strongest claim

Safety is proved: fewer than N/3 Byzantine validators cannot cause conflicting finalization, independent of Phase 1 clustering or tree topology.

C2weakest assumption

The specific 8-dimensional vector-sum construction actually produces distances proportional to disagreement and exact weighted means for arbitrary transaction sets, as required for the distance-filtering and clustering steps to be safe.

C3one line summary

Distance-preserving digests based on 8D vector sums replace hashes in BFT protocols to enable distance-aware voting, smaller tree structures, and efficient cross-shard checks while maintaining safety under N/3 faults.

References

22 extracted · 22 resolved · 0 Pith anchors

[1] HotStuff: BFT Consensus with Linearity and Responsiveness, 2019

[2] Practical Byzantine Fault Tolerance, 1999

[3] Short Signatures from the Weil Pairing, 2004

[4] blst: BLS12-381 signature library,

[5] Ethereum 2.0 Beacon Chain Specification,

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:52.889519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce8d71029a77a08abe8cb40606e4c8b0502e60ee0b9551203cf6f09ccc073baf

Aliases

arxiv: 2605.15329 · arxiv_version: 2605.15329v1 · doi: 10.48550/arxiv.2605.15329 · pith_short_12: Z2GXCAU2O6QI · pith_short_16: Z2GXCAU2O6QIVPUM · pith_short_8: Z2GXCAU2

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/Z2GXCAU2O6QIVPUMWQDANZGIWB \
  | 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: ce8d71029a77a08abe8cb40606e4c8b0502e60ee0b9551203cf6f09ccc073baf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38331133bf42fb8372f760eec387862234c4b58a4f434a4fc42a6aaec25a4fe2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CR",
    "submitted_at": "2026-05-14T18:44:04Z",
    "title_canon_sha256": "c963f36f18ed09b545cd7712d33e261b7b2142e542e90a04b6c77d88dfbf05f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15329",
    "kind": "arxiv",
    "version": 1
  }
}