Pith Number

pith:QERZJDRI

pith:2026:QERZJDRIBAXUJHH7LVNGQCTXKX

not attested not anchored not stored refs resolved

Mathematical Informatics: Algorithms

JFLI), Thomas Seiller (CNRS

Algorithms are defined as finite directed graphs whose edges are labelled by partial maps over an abstract data structure.

arxiv:2605.18342 v1 · 2026-05-18 · cs.LO

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\usepackage{pith}
\pithnumber{QERZJDRIBAXUJHH7LVNGQCTXKX}

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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

We introduce a formal notion of algorithm as a finite directed graph whose edges are labelled by partial maps over an abstract data structure. This yields a precise notion of implementation and situates algorithms as abstract partial specifications of computational behaviour.

C2weakest assumption

That models of computation can be uniformly described as monoid actions on a configuration space and that programs are dynamical systems constrained by this action, allowing a correspondence between computational steps and labelled graph transitions that preserves induced transformations on data representations.

C3one line summary

Algorithms are defined as finite directed graphs with edges labelled by partial maps on abstract data structures, with programs implementing them via step correspondences that preserve data transformations in monoid-action models.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Polity Press (2022), https://books.google.fr/books?id=sIVdzgEACAAJ 2022

[2] Anh-Ton Le, H.L., Valarcher, P.: Completeness of Seiller ’s Abstract Machine (2025), https://hal.u-pec.fr/hal-05137612 , preprint 2025

[3] Computational Complexity 2 (1992), https://doi.org/10.1007/BF01201998 1992 · doi:10.1007/bf01201998

[4] Bulletin of the European Association for Theoretical Computer Science (2003) 2003

[5] Blass, A., Dershowitz, N., Gurevich, Y.: When are two algo rithms the same? CoRR abs/0811.0811 (2008), http://arxiv.org/abs/0811.0811 2008

Receipt and verification

First computed	2026-05-20T00:05:56.020880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8123948e28082f449cff5d5a680a7755c7ab99f091379a18f4f76da891448b21

Aliases

arxiv: 2605.18342 · arxiv_version: 2605.18342v1 · doi: 10.48550/arxiv.2605.18342 · pith_short_12: QERZJDRIBAXU · pith_short_16: QERZJDRIBAXUJHH7 · pith_short_8: QERZJDRI

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/QERZJDRIBAXUJHH7LVNGQCTXKX \
  | 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: 8123948e28082f449cff5d5a680a7755c7ab99f091379a18f4f76da891448b21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5168552f62fb5c4a4b0f7842b5c378f2bd22e78a51f6707a2b5723652a5e540a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-18T12:55:40Z",
    "title_canon_sha256": "24d66edae42993869d4f23b96d1a54dd910d0e18d16b225d3502aad13f3e1ffe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18342",
    "kind": "arxiv",
    "version": 1
  }
}