# Verification report — OWR-14299911-020 (Genevois: the travelling polytope constant of a product of trees)

Verification date: 2026-10-17.

**Verdict.** The note answers the products-of-trees instance of the question; every statement it makes is proved.
- **Settled.** For trees T_1, …, T_d, of which exactly d′ ≥ 1 have unbounded diameter, TP(T_1 × … × T_d) = d′/(2d′ − 1);
  no bound on the degrees is needed (Theorem 1.2(a)). In particular a product of d regular trees of degree at
  least 2 has constant d/(2d − 1), and the constant is 1 when exactly one factor is unbounded. If all factors
  have finite diameter, the constant is 1 for an infinite product and every exponent is admissible for a finite
  one (Theorem 1.2(b), (c)). This answers Question 12.17 of Genevois's thesis (TS(T_1 × T_2) for two trees) in
  all cases, confirms the guess of his Question 12.16 for products of regular trees, and gives a positive
  answer to his Question 12.18 for products of trees (Corollary 1.3).
- **Not new.** The constant (Genevois's travelling salesman constant TS(X), thesis Definition 9.38), the formula
  TP(x,F,y) = 2·#(hyperplanes separating two points of F ∪ {x,y}) (thesis Remark 9.39), the inequality
  TP ≤ 2TS (source; thesis Claim 9.43), the bounds TP ∈ [1/2, 2/3] ∪ {1}, the value d/(2d − 1) for Z^d and the
  family of sets used for the upper bound (thesis Lemma 9.50) are Genevois's. The strip bound (Lemma 3.2) is
  classical (Few 1955). What the note adds is the lower bound of Proposition 3.3 for products of trees (Euler-tour
  covering of the projected hulls) and, with it, the values for products of trees.
- **No new value.** d/(2d − 1) and 1 were known values of the constant (Z^d; hyperbolic graphs), so the note gives
  no new value in answer to the source's main question.
- **Open.** Which values the constant takes on median graphs (the source's question, record OWR-14299911-019);
  the behaviour of the constant under products of other median graphs (the clause "more generally determine how
  this constant behaves under products of median graphs" of the Hugging Face statement of OWR-14299911-020). The
  note records only the upper bound d/(2d − 1) for products of d median graphs of unbounded diameter (Section 6).

Three independent verification runs, all AI-assisted, examined the result: runs A and B the first written
account, the third run the text of the note, including the case of factors of finite diameter. None found a
mathematical error. The note is unrefereed.

## Statement checked
- **Primary source.** A. Genevois, Problem 7 "Travelling polytopes", in: Median Geometry and Applications,
  Oberwolfach Reports 23 (2026), no. 1, Report No. 8/2026, pp. 487–540, doi:10.4171/OWR/2026/8 (Crossref:
  published 2026-07-21; organizers G. Arzhantseva, I. Chatterji, E. Fioravanti, G. Niblo; workshop 15–20
  February 2026). Problem 7 is on pp. 530–531 (PDF pages 44–45 of the open-access file); the problem session runs
  over pp. 528–536; Genevois's talk abstract "An invitation to quasi-median graphs" is on pp. 507–510.
  - Definitions: TS(x,F,y), the shortest length of a path from x to y through all vertices of F; TP(x,F,y), the
    shortest length of a path of polytopes P_0 = {x}, …, P_k = {y} covering F, where a polytope is the convex hull
    of finitely many vertices and consecutive polytopes satisfy P = hull(Q ∪ {u}) with u ∈ ∂Q;
    TP(X) = sup{α | ∃C > 0 ∀x, y, F: TP(x,F,y) + |F| ≥ C(TS(x,F,y) + |F|)^α}.
  - Known facts listed without references, for unbounded median graphs of bounded degree:
    TP(X) ∈ [1/2, 2/3] ∪ {1}; TP(X) = 1 iff X is hyperbolic; TP(X) = 1/2 for infinite cubical dimension;
    TP(E^d) = d/(2d − 1).
  - The question: which values TP takes on median graphs; for instance, compute the travelling polytope constant of
    a product of (regular) trees.
  - Checked against the open-access file by the first written account and by both verification runs (run A from
    page images).
- **Corpus record.** ulamai/UnsolvedMath, OWR-14299911-020 (dataset version 1.6.0; status open). Hugging Face
  title "Travelling-Polytope Constants for Products of Trees"; statement: compute TP(X) when X is a product of
  regular trees, and more generally determine how this constant behaves under products of median graphs. The raw
  extraction in the corpus glues the end of Problem 7 to the beginning of Problem 8; record -018 holds the
  definitions and record -019 the question "which values".
- **The same constant in print.** A. Genevois, PhD thesis (Université Aix-Marseille, 2017), arXiv:1712.01618 v1:
  Section 9.1 (graph FS(X) of finite convex subcomplexes; Fact 9.1, Remark 9.5, Proposition 9.6), Section 9.4
  (Theorem 9.37, Definition 9.38, Remark 9.39, Claim 9.43, Lemma 9.44, Proposition 9.45, Lemma 9.46, Lemma 9.50,
  Corollaries 9.52–9.53) and Questions 12.16–12.18 on p. 248; A. Genevois, Proc. Edinb. Math. Soc. 65 (2022)
  500–529, doi:10.1017/S0013091522000190 (read as arXiv:1705.00834 v2), Sections 3.2 and 4.2 (Proposition 4.6,
  Lemma 4.7); A. Genevois, arXiv:2604.06686 v1, Section 3.1 (Definition 3.3, Lemma 3.4, Claim 3.5, Proposition
  3.8, Lemma 3.9).

## Readings
| Reading | Answer | Where |
|---|---|---|
| "Path" through F in TS | a walk (a path without repeated vertices may not exist); TS = minimum over orderings of F | Definition 1.1(a) |
| u ∈ ∂Q | outer vertex boundary; this is Genevois's notation ∂_B A (arXiv:2604.06686, Lemma 3.4) and gives the edges of his graph FS(X) (thesis Remark 9.5). With u arbitrary, TP(x,F,y) ≤ 2|F| + 2 and TP(X) = 0 for every unbounded graph | Section 1.1 |
| Normalisation: (TS + \|F\|)^α (source) versus TS^α (thesis, PEMS) | the same admissible exponents in (0, 1], and no α > 1 is admissible for infinite graphs in either; so the constants coincide for infinite median graphs | Lemma 2.6(b), (c) |
| "Product of (regular) trees" | Cartesian product; regular trees of degree ≥ 2 (degree 2 gives Z); the theorem holds for all trees, of any degrees | Theorem 1.2, Corollary 1.3(a) |
| Factors of finite diameter | d′ counts the unbounded factors; the value is d′/(2d′ − 1), 1 if d′ = 0 and X is infinite, and every exponent is admissible if X is finite | Theorem 1.2 |
| HF clause "more generally … products of median graphs" | not answered; only the upper bound d/(2d − 1) for products of d unbounded median graphs | Section 6 |
| Source's main question "which values can TP take" | not answered; the note gives no new value | Section 1.4, "Scope and priority" |

## Results in the paper
- **Lemma 2.1.** Convex sets of a product of trees are the products of subtrees; hull = product of the hulls of
  the projections; polytopes = products of finite subtrees.
- **Lemma 2.3.** A step of a path of polytopes adds (or removes) one leaf in one factor.
- **Proposition 2.4** (Genevois, thesis Remark 9.39, reproved for products of trees). TP(x,F,y) = 2 hyp(F ∪ {x,y}),
  hyp = Σ_i (|H_i| − 1). Remark 2.5: the extension to median graphs, with citations.
- **Lemma 2.6.** (a) TP ≤ 2TS in every connected graph; (b) no α > 1 is admissible in an infinite graph;
  (c) equivalence of the two normalisations for α ∈ (0, 1].
- **Lemma 3.1** (Euler tour): a 1-Lipschitz surjection {0, …, 2h − 2} → V(H) for a tree H with h vertices.
- **Lemma 3.2** (strip method, Few 1955): in [0, L]^k, an ordering of n points between a and b with ℓ¹-length
  ≤ c_k(n^(1−1/k) + 1)L, c_k = (k+1)2^(k−1) + k.
- **Proposition 3.3** (lower bound; the new part). If T_{k+1}, …, T_d have finite diameter with sum D, then
  TP + |F| ≥ (TS + |F|)^(k/(2k−1))/(4c_k + 2D + 1); for D = 0, C = 1/(4c_d + 1) (1/13, 1/33, …).
- **Proposition 4.1** (upper bound; Genevois's family of thesis Lemma 9.50 on geodesic segments). If T_1, …, T_k
  are unbounded, then for every n ≥ 2 a set F of n^k vertices has TP + |F| ≤ (2k+1)n^k and TS + |F| ≥ n^(2k−1).
- **Theorem 1.2 and Corollary 1.3** as in the verdict. **Remark 5.1:** for T × K with K of diameter D,
  TS ≤ (3/2)TP + D(|F| + 1); for K = K_2, TS ≤ (3/2)TP + |F| + 1.
- **Section 6:** products of median graphs: upper bound d/(2d − 1) when all factors are unbounded (no convexity of
  the segments needed); the lower bound for products of hyperbolic factors would need a covering walk bound, which
  thesis Lemma 9.46 provides for uniformly locally finite hyperbolic complexes; this extension is not claimed.

## Computations (sanity checks; programs and outputs in reproducibility/)
No proof depends on a computation.
- **Program of the note** (`check_note.py`, standard library, about 4 s; 354,889 checks, 0 failures). Part A:
  constants and exact identities (c_k, C, exponents, the integer facts n ≤ m^k ≤ 2^k n for 2 ≤ k ≤ 6,
  n ≤ 20,000, the counting inequalities of Proposition 4.1). Part B: Lemmas 2.1 and 2.3, Proposition 2.4 and
  Lemma 2.6(a) by a literal brute force from the definitions on eight products of trees with at most 16 vertices,
  for all x, y and all F with |F| ≤ 2 plus random F with |F| ∈ {3, 4} (115,394 triples; the wrong formula
  TP = hyp is rejected). Part C: Lemma 3.1 on all 201 trees with at most 10 vertices and 200 random trees.
  Part D: Lemma 3.2 on 1,000 point sets in exact rational arithmetic. Part E: the walk of the proof of
  Proposition 3.3 and each of its bounds on 1,200 random triples in products of up to four trees, with and without
  factors of finite diameter, the final inequality in integer arithmetic. Part F: Proposition 4.1 on nine
  instances (exact TS; literal TP in seven). Part G: the bound of Theorem 1.2(b) on 400 triples.
- **Programs with which the result was first obtained** (`original/`): a literal brute force of TP, TS and hyp on
  five small median graphs (including the L-shaped median graph, not a product of trees); exact values for the
  family of Proposition 4.1 in four cases; a random test of Proposition 3.3 in Z² (F now drawn as a set; printed
  output unchanged).
- **Verification run A** (`verification_run_A/`): literal brute force on six products of trees (17,760 triples)
  and three other median graphs (900 triples); Lemma 3.1 on 300 random trees; Lemma 3.2 on 1,600 point sets;
  legality of every step of the box path of Proposition 4.1 in four cases; literal TP and exact TS for the family.
- **Verification run B** (`verification_run_B/`): literal brute force of TP on 875,033 triples in 20 median graphs
  with negative controls (non-median graphs, wrong hull, wrong formulas, other readings of ∂Q, corrupted TS), all
  detected; the family of Proposition 4.1 in six cases (literal TP in five); every inequality of the proof of
  Proposition 3.3 on 2,100 random triples; Lemma 3.2 on 12,000 point sets; hill climbing; the exponent test up to
  n = 2^30.
- **Third verification run** (`independent_run_2/`, two programs, standard library): `r2_literal.py` (34 s;
  1,059,061 checks, 0 failures): literal brute force with generic graph code; equation (2), Lemma 2.1 (convex sets
  of 15 products of one to three trees = products of subtrees, also against all subsets for ≤ 16 vertices),
  Lemma 2.3 on every step, Proposition 2.4 on 465,402 triples (products with stars, P2 or K1,2 next to longer
  factors among them), Lemma 2.6(a) also in seven graphs that are not median (C5, C6, C7, K2,3, K4, Petersen, a
  random graph), Remark 2.5 on five other median graphs, the upper bound of Section 6 on non-convex staircase
  segments, Proposition 4.1 with k < d (literal TP in four products), controls. `r2_chain.py` (8 s; 295,262
  checks, 0 failures): exact arithmetic; constants and integer facts; Lemma 3.1 as built in the proof on all
  18,249 labelled trees with at most 7 vertices; Lemma 3.2 on 6,000 point sets; **every link of the proof of
  Proposition 3.3 on 6,000 random triples in products of up to five trees, with factors of finite diameter
  (D > 0) in two thirds of them**, final inequality in exact integer form; **Proposition 4.1 with 1 or 2 extra
  factors of finite diameter** (exact TS up to N = 16); Theorem 1.2(b) on 1,500 triples; the walk of Remark 5.1
  on 1,200 triples; hill climbing (largest ratio 1.38 against at least 13 allowed).
- **Re-run.** On 2026-10-17 every program of the package was run again from a copy of the package; all outputs are
  identical to the recorded ones up to dates, running times and lines written by the shell
  (`reproducibility/RERUN_LOG.txt`). The third verification run ran all eight programs again from the extracted
  archive `source.zip`, with the same result (`reproducibility/independent_run_2/package_rerun/RERUN_LOG.txt`).

## Independent verification runs
The result was first written up, for products of trees of unbounded diameter, with two programs, on 2026-10-17. Two independent verification runs, both AI-assisted, followed the same day; each wrote its own
programs and did not see the other's report. Run A examined the statement, the proofs and the computations, and
read the thesis, the PEMS paper and arXiv:2604.06686; run B examined the proofs, computed independently, and
searched the literature and checked the bibliography.

| Item | Run A | Run B |
|---|---|---|
| Statement and conventions against the source (reading of ∂Q, walks, normalisation) | CONFIRMED (page images; ∂Q confirmed by Genevois's notation in 2604.06686 and thesis FS(X)) | CONFIRMED (own extraction; controls on other readings of ∂Q) |
| Lemmas 2.1, 2.3 (convex sets, one step) | CONFIRMED (re-derived; brute force) | CONFIRMED (re-derived; enumeration) |
| Proposition 2.4 (TP = 2 hyp) | CONFIRMED; median version re-derived via gates | CONFIRMED; 875,033 triples; known (thesis Remark 9.39) |
| Lemmas 3.1, 3.2 (Euler tour, strip bound) | CONFIRMED (all constants re-derived; tests) | CONFIRMED (12,000 point sets) |
| Proposition 3.3 with D = 0 (lower bound) | CONFIRMED (C_1 = 1/13, C_2 = 1/33; N = 0 case) | CONFIRMED (every link tested on 2,100 triples) |
| Proposition 4.1 with k = d (upper bound) | CONFIRMED (counts, legality of the box path, limit) | CONFIRMED (family computed exactly) |
| Normalisation TP(X) = thesis TS(X) | PROVED (two-line argument) | CONFIRMED |
| Cases with factors of finite diameter | two trees: PROVED (one unbounded factor gives 1; both bounded: 1 or degenerate) | suggested to prove or mark as heuristic |
| Side remark (b) of the first account (convex segments needed) | WRONG as stated (convexity not needed); harmless | — |
| Side remark on T × K_2 | correct in substance; the walk did not end at y (+1 needed) | same observation (final leg missing) |
| Literature and novelty | MATERIALLY INCOMPLETE: thesis, PEMS 2022 and 2604.06686 missed; "unpublished" wrong | WRONG IN SUBSTANCE for the same reasons; main theorem not found in print |
| Classification | theorem PROVED; record PARTIAL | theorem PROVED; record PARTIAL |

Neither run found an error in the proofs of the theorem.

**Corrections required by runs A and B**, all applied in the note:
1. (A1, B1) The literature: thesis Section 9.1, Definition 9.38, Remark 9.39, Lemmas 9.44, 9.46, 9.50,
   Proposition 9.45, Corollaries 9.52–9.53, Questions 12.16–12.18; PEMS 2022 Sections 3.2 and 4.2, Lemma 4.7;
   arXiv:2604.06686 Section 3.1 — Sections 1.2 and 1.4, Remark 2.5, "Scope and priority".
2. (A2) "The known facts … appear to be unpublished" is not in the note; the facts are cited to the thesis and
   PEMS 2022, and the source is said to list them without references.
3. (A3, B1) The question is identified as thesis Question 12.17 (2017), posed again in 2026; the note confirms the
   guess of Question 12.16 for products of regular trees (Corollary 1.3(a)); the normalisation argument is
   Lemma 2.6(b), (c).
4. (A4, B2) The exact formula and the lower bound 1/2 are presented as known; Proposition 4.1 is presented as
   Genevois's family of Lemma 9.50 on geodesic segments, and Lemma 3.2 as the strip method; the new part is
   Proposition 3.3. The partial unavailability of the arXiv interface, OpenAlex and Semantic Scholar is stated.
5. (A5, B3) Record status: partial (products of trees answered; "which values" and general products open);
   "HF clean statement" instead of "corpus title" in this report.
6. (A6) Remark (c) of the first account (lower bound for hyperbolic factors) is cited to thesis Lemma 9.46 and not
   claimed (Section 6).
7. (A7) Remark (b) corrected: no convexity of the segments is needed (Section 6).
8. (A8) The T × K_2 walk now ends at y: TS ≤ (3/2)TP + |F| + 1 (Remark 5.1); page ranges pp. 528–536 (problem
   session) and pp. 507–510 (abstract); a reference to an earlier unpublished triage note, criticised by run A, is not used;
   F drawn as a set in the package program.
9. (A9) The remaining cases of Question 12.17: Theorem 1.2(a) with d′ = 1, (b), (c), Corollary 1.3(b).
10. (B suggestions) Few 1955, Djoković 1973, Winkler 1984 cited; Erschler–Mitrofanov cited in the journal version
    (Geom. Dedicata 217 (2023)); full data for Sageev 1995 and Chepoi 2000; the median remark has its one-line
    justification (Remark 2.5).

**Changes made when the note was written, after runs A and B.**
- The theorem is stated for products in which some factors have finite diameter (d′ unbounded factors give
  d′/(2d′ − 1)); Proposition 3.3 carries the extra term 2D, and Proposition 4.1 places the family in the unbounded
  factors only. For two factors this was proved by run A; the general case was written for the note and was then
  examined by the third verification run (next section), which found it correct.
- TP ≤ 2TS is proved for every connected graph (Lemma 2.6(a)), and the absence of exponents α > 1 for every
  infinite graph (Lemma 2.6(b)).

## Third verification run (2026-10-17, on the text of the note)
A third independent verification run, AI-assisted, examined the text of the note (11 pages before this run,
12 after). It did not write the note. It downloaded and read the sources itself (OWR 8/2026: Problem 7 as a page
image, the problem session pp. 528–536 and Genevois's abstract pp. 507–510; the thesis arXiv:1712.01618 v1,
Section 9.1, Definition 9.38 to Corollary 9.53, Questions 12.16–12.18 on p. 248; PEMS 2022 as arXiv:1705.00834 v2,
Sections 3.2 and 4.2; arXiv:2604.06686 v1, Section 3.1), compared every statement that the note quotes from them,
re-derived every proof line by line with the case of factors of finite diameter first, wrote two programs before
reading those of the package (Computations above), ran the whole package again from the archive, repeated the
literature search, verified the eight DOIs on Crossref, and inspected every rendered page.

| Item | Third run |
|---|---|
| Statement, readings (∂Q also as ∂_X Y in arXiv:2604.06686, Claim 3.5), scope | CONFIRMED |
| Lemmas 2.1, 2.3, Proposition 2.4, Remark 2.5, Lemma 2.6 | CONFIRMED (re-derived; literal search on 465,402 triples; Lemma 2.6(a) also in non-median graphs) |
| Lemmas 3.1, 3.2 and Proposition 3.3 with D = 0 | CONFIRMED (re-derived; exact tests) |
| **Proposition 3.3 with D > 0, Proposition 4.1 with k < d, Theorem 1.2(a) with d′ < d** | **CONFIRMED** (re-derived in full; every link of the proof tested exactly on 4,000 triples with D > 0; Proposition 4.1 with extra factors, literal TP in four products, exact TS in ten cases) |
| Theorem 1.2(b), (c), Corollary 1.3 (Questions 12.16–12.18 checked on p. 248) | CONFIRMED |
| Remark 5.1, Section 6 (upper bound also for non-convex segments; lower bound not claimed) | CONFIRMED |
| Quoted statements of the thesis, PEMS 2022, arXiv:2604.06686 and OWR 8/2026 | CONFIRMED; three sentences made more precise |
| Novelty and credit | no earlier answer found; credit complete; claims hedged |
| Package re-run from `source.zip` | all eight programs exit 0; outputs identical up to dates, times and shell lines |

It found no mathematical error and no gap. **Corrections it required**, all applied:
1. The paragraph "Verification" records this run, including its examination of the case of factors of finite
   diameter (the earlier sentence that this case had not been examined by an independent run was removed), and
   Section 7 lists the programs of the three runs.
2. Abstract: d′ ≥ 1 is defined as the number of factors of unbounded diameter.
3. Section 1.1: the reading of ∂Q cites arXiv:2604.06686, Lemma 3.4 and Claim 3.5 (notation ∂_X Q).
4. After Proposition 4.1: the sets F are those of thesis Lemma 9.50 "up to the range of the indices" (the thesis
   uses 0 ≤ k_i ≤ n, the note 0 ≤ m_i ≤ n − 1).
5. After Theorem 1.2: the sentence that the source "excludes" bounded graphs was replaced by "the known values
   listed in [Gen26a] concern unbounded graphs" (the source does not restrict its question).
6. "Scope and priority" records the searches of this run and that the publisher's file of Few (1955) could not
   be accessed.
7. Package: `reproducibility/independent_run_2/` with a README; `reproducibility/README.md` and this report
   updated.
8. Zenodo metadata: publication date 2026-10-17 (it was 2026-10-16), the description is the final abstract, and
   the checksums were recomputed.

## Relation to the literature, novelty and scope
- **Searches (2026-10-17).** The first written account: the source (the problem session read; all 54 pages
  searched), the arXiv listing of all 75 entries for author Genevois (up to arXiv:2608.24725 of 2026-08-25),
  arXiv keyword queries, zbMATH, Crossref, two web searches, the full texts of arXiv:2605.20419 and 2608.24725.
  Run A: the thesis, PEMS 2022 and arXiv:2604.06686 in full text (relevant parts read), zbMATH author listing,
  Crossref, one web search. Run B: the same texts, zbMATH (65 hits for "travelling polytope", all on TSP
  polytopes), works citing the OWR report (OpenAlex, Semantic Scholar, Crossref: none), four web searches. When
  the note was written: Crossref records of all cited DOIs (eight requests); the arXiv interface refused two
  requests (HTTP 429) and was not used further. Third run: the arXiv website list of Genevois's preprints (67
  entries, the latest arXiv:2608.24725 of 25 August 2026, nothing newer on 17 October 2026) and keyword searches
  ("salesman" with "median"; "travelling/traveling polytope"; "travelling/traveling salesman constant", which
  only finds the Beardwood–Halton–Hammersley constant; "salesman" with "cube complex"), the arXiv export API
  (HTTP 429, also after a wait), Crossref (eight DOIs, two keyword queries), OpenAlex (the report: cited by 0;
  further queries refused by the daily limit), zbMATH Open (Genevois's twelve documents of 2026, keyword
  queries), Semantic Scholar (64 works citing the thesis, none on the constant), one web search.
  - No paper computing the constant for products of trees, or answering thesis Question 12.17, was found.
  - Closest work on a different question: Erschler–Mitrofanov, Geom. Dedicata 217 (2023), Paper No. 68 (orderings
    of metric spaces efficient for the travelling salesman problem); no polytopes.
- **What was read.** The source in the open-access file; the thesis in arXiv version v1 (Sections 9.1 and 9.4,
  Questions 12.16–12.18); PEMS 2022 in arXiv version v2 (Sections 3.2 and 4.2; the journal version was not
  compared); arXiv:2604.06686 v1 (Section 3.1); of Erschler–Mitrofanov the abstract. Few (1955), Djoković (1973),
  Winkler (1984), Sageev (1995) and Chepoi (2000) are cited for classical facts and were not read for the note
  (the publisher's file of Few (1955) refused the third run's automated request).
  Only the results reproved in the note were checked; the other quoted results of Genevois were not re-proved.
- **Caveats.** The arXiv interface, OpenAlex and Semantic Scholar were partly unavailable because of rate limits.
  A search that finds nothing is not a proof of novelty; no priority is claimed. The value d/(2d − 1) was already
  known for Z^d, and the argument is a short extension of the proposer's own Lemma 9.50.
- **Scope.** The note answers the products-of-trees instance of the source's question and thesis Question 12.17.
  The source's main question and the HF clause on general products of median graphs remain open.

## Public release and license
This paper, its source files, and this verification report are licensed under the Creative Commons Attribution
4.0 International License (CC BY 4.0): https://creativecommons.org/licenses/by/4.0/