Pith Number

pith:ZFDK4KUW

pith:2026:ZFDK4KUWEPNNLRRAG255Q7S52N

not attested not anchored not stored refs resolved

Mayer Path Homology

Dilan Karaguler, Guo-Wei Wei

Mayer path homology equips directed path complexes with an N-nilpotent differential to produce a finer invariant than standard path homology.

arxiv:2605.16525 v1 · 2026-05-15 · math.AT

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

This construction defines a canonical invariant of directed graphs and is more sensitive than standard path homology, distinguishing directed network motifs that ordinary path homology cannot separate.

C2weakest assumption

The N-nilpotent differential on path complexes produces well-defined homology groups that remain invariant under the directed graph structure and are strictly finer than classical path homology.

C3one line summary

Mayer path homology equips path complexes with an N-differential to yield homology groups that distinguish directed graph motifs more finely than standard path homology.

References

20 extracted · 20 resolved · 1 Pith anchors

[1] Path topology in molecular and materials sciences.The journal of physical chemistry letters, 14(4):954–964, 2023 2023

[2] Samir Chowdhury and Facundo M´ emoli.Persistent Path Homology of Directed Networks, pages 1152–1169

[3] Dey, Tianqi Li, and Yusu Wang 2022

[4] Mayer-homology learning predic- tion of protein-ligand binding affinities.Journal of computational biophysics and chemistry, 24(02):253–266, 2025 2025

[5] Network modeling and topology of aging.Physics Reports, 1101:1–65, 2025 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:27.341842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c946ae2a9623dad5c62036bbd87e5dd369f35446daefe6b520a0cec5d01979d9

Aliases

arxiv: 2605.16525 · arxiv_version: 2605.16525v1 · doi: 10.48550/arxiv.2605.16525 · pith_short_12: ZFDK4KUWEPNN · pith_short_16: ZFDK4KUWEPNNLRRA · pith_short_8: ZFDK4KUW

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/ZFDK4KUWEPNNLRRAG255Q7S52N \
  | 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: c946ae2a9623dad5c62036bbd87e5dd369f35446daefe6b520a0cec5d01979d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50031f932e63c4f58f9b3de84fcf182be561c9e00d7e51288fffd9a4acfe3b81",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-05-15T18:21:42Z",
    "title_canon_sha256": "1be795c64949c265b1588e906b458ae5084b613e9ab1b2197c03afbe28f7e945"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16525",
    "kind": "arxiv",
    "version": 1
  }
}