# Question 22025: Every Target Open Must Have an Open Source Preimage

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0043-22025 · q-20261014-advance-20261110-r03-continuous-image-of-compact-0050



## Original question and givens

Use complete source carrier Fin(3)={0,…,2} with topology=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]], target carrier Fin(3)={0,…,2} with topology=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]], total map=[0, 2, 2] and source subset K=[0, 1, 2]. The source/target topologies must qualify; continuity is tested by every target-open preimage. K is compact by finiteness, including empty K. Give (open_preimage_rows, continuous, certificate).


- G001 — Use complete source carrier Fin(3)={0,…,2} with topology=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]], target carrier Fin(3)={0,…,2} with topology=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]], total map=[0, 2, 2] and source subset K=[0, 1, 2]. The source/target topologies must qualify; continuity is tested by every target-open preimage. K is compact by finiteness, including empty K. Give (open_preimage_rows, continuous, certificate).





## Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.


- [mko-continuous-image-of-compact](https://ocme.evemisslab.com/en/mko/mko-continuous-image-of-compact/)





## Step-by-step derivation

S001 · impliesBefore

source operation=compactimg-continuity-audit;original snapshot and mathematics retained

After

explicit ordered source output fields=[open_preimage_rows, continuous, certificate]

Conditions: none

Retain the historical interface marker and list ordered source fields without JavaScript.MVT fields come from the original mode,without padding or answer-shape inference.Tags and fixed No markers retain their claim scope.

Step identifiers and dependenciesRule: source_ordered_interface_explicit_without_javascript · Uses: G001





S002 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=0,U=[]

After

ALL [other_open_index,union,intersection] rows=[[0, [], []], [1, [0], []], [2, [0, 1], []], [3, [0, 1, 2], []], [4, [0, 2], []], [5, [1], []], [6, [1, 2], []], [7, [2], []]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S001





S003 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=1,U=[0]

After

ALL [other_open_index,union,intersection] rows=[[0, [0], []], [1, [0], [0]], [2, [0, 1], [0]], [3, [0, 1, 2], [0]], [4, [0, 2], [0]], [5, [0, 1], []], [6, [0, 1, 2], []], [7, [0, 2], []]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S002





S004 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=2,U=[0, 1]

After

ALL [other_open_index,union,intersection] rows=[[0, [0, 1], []], [1, [0, 1], [0]], [2, [0, 1], [0, 1]], [3, [0, 1, 2], [0, 1]], [4, [0, 1, 2], [0]], [5, [0, 1], [1]], [6, [0, 1, 2], [1]], [7, [0, 1, 2], []]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S003





S005 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=3,U=[0, 1, 2]

After

ALL [other_open_index,union,intersection] rows=[[0, [0, 1, 2], []], [1, [0, 1, 2], [0]], [2, [0, 1, 2], [0, 1]], [3, [0, 1, 2], [0, 1, 2]], [4, [0, 1, 2], [0, 2]], [5, [0, 1, 2], [1]], [6, [0, 1, 2], [1, 2]], [7, [0, 1, 2], [2]]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S004





S006 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=4,U=[0, 2]

After

ALL [other_open_index,union,intersection] rows=[[0, [0, 2], []], [1, [0, 2], [0]], [2, [0, 1, 2], [0]], [3, [0, 1, 2], [0, 2]], [4, [0, 2], [0, 2]], [5, [0, 1, 2], []], [6, [0, 1, 2], [2]], [7, [0, 2], [2]]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S005





S007 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=5,U=[1]

After

ALL [other_open_index,union,intersection] rows=[[0, [1], []], [1, [0, 1], []], [2, [0, 1], [1]], [3, [0, 1, 2], [1]], [4, [0, 1, 2], []], [5, [1], [1]], [6, [1, 2], [1]], [7, [1, 2], []]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S006





S008 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=6,U=[1, 2]

After

ALL [other_open_index,union,intersection] rows=[[0, [1, 2], []], [1, [0, 1, 2], []], [2, [0, 1, 2], [1]], [3, [0, 1, 2], [1, 2]], [4, [0, 1, 2], [2]], [5, [1, 2], [1]], [6, [1, 2], [1, 2]], [7, [1, 2], [2]]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S007





S009 · impliesBefore

SOURCE:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=7,U=[2]

After

ALL [other_open_index,union,intersection] rows=[[0, [2], []], [1, [0, 2], []], [2, [0, 1, 2], []], [3, [0, 1, 2], [2]], [4, [0, 2], [2]], [5, [1, 2], []], [6, [1, 2], [2]], [7, [2], [2]]];empty/full opens present;every result in SAME SOURCE topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S008





S010 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=0,U=[]

After

ALL [other_open_index,union,intersection] rows=[[0, [], []], [1, [0], []], [2, [0, 1], []], [3, [0, 1, 2], []], [4, [0, 2], []], [5, [1], []], [6, [1, 2], []], [7, [2], []]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S009





S011 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=1,U=[0]

After

ALL [other_open_index,union,intersection] rows=[[0, [0], []], [1, [0], [0]], [2, [0, 1], [0]], [3, [0, 1, 2], [0]], [4, [0, 2], [0]], [5, [0, 1], []], [6, [0, 1, 2], []], [7, [0, 2], []]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S010





S012 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=2,U=[0, 1]

After

ALL [other_open_index,union,intersection] rows=[[0, [0, 1], []], [1, [0, 1], [0]], [2, [0, 1], [0, 1]], [3, [0, 1, 2], [0, 1]], [4, [0, 1, 2], [0]], [5, [0, 1], [1]], [6, [0, 1, 2], [1]], [7, [0, 1, 2], []]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S011





S013 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=3,U=[0, 1, 2]

After

ALL [other_open_index,union,intersection] rows=[[0, [0, 1, 2], []], [1, [0, 1, 2], [0]], [2, [0, 1, 2], [0, 1]], [3, [0, 1, 2], [0, 1, 2]], [4, [0, 1, 2], [0, 2]], [5, [0, 1, 2], [1]], [6, [0, 1, 2], [1, 2]], [7, [0, 1, 2], [2]]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S012





S014 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=4,U=[0, 2]

After

ALL [other_open_index,union,intersection] rows=[[0, [0, 2], []], [1, [0, 2], [0]], [2, [0, 1, 2], [0]], [3, [0, 1, 2], [0, 2]], [4, [0, 2], [0, 2]], [5, [0, 1, 2], []], [6, [0, 1, 2], [2]], [7, [0, 2], [2]]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S013





S015 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=5,U=[1]

After

ALL [other_open_index,union,intersection] rows=[[0, [1], []], [1, [0, 1], []], [2, [0, 1], [1]], [3, [0, 1, 2], [1]], [4, [0, 1, 2], []], [5, [1], [1]], [6, [1, 2], [1]], [7, [1, 2], []]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S014





S016 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=6,U=[1, 2]

After

ALL [other_open_index,union,intersection] rows=[[0, [1, 2], []], [1, [0, 1, 2], []], [2, [0, 1, 2], [1]], [3, [0, 1, 2], [1, 2]], [4, [0, 1, 2], [2]], [5, [1, 2], [1]], [6, [1, 2], [1, 2]], [7, [1, 2], [2]]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S015





S017 · impliesBefore

TARGET:ORIGINAL carrier Fin(3);complete canonical opens=[[], [0], [0, 1], [0, 1, 2], [0, 2], [1], [1, 2], [2]];open index=7,U=[2]

After

ALL [other_open_index,union,intersection] rows=[[0, [2], []], [1, [0, 2], []], [2, [0, 1, 2], []], [3, [0, 1, 2], [2]], [4, [0, 2], [2]], [5, [1, 2], []], [6, [1, 2], [2]], [7, [2], [2]]];empty/full opens present;every result in SAME TARGET topology

Conditions: none

Keep source and target carriers distinct.Check all open pairs and empty/full membership.Any union in a finite family reduces to finitely many distinct opens;a finite image does not bypass topology or continuity obligations.

Step identifiers and dependenciesRule: compactimg_qualified_complete_source_or_target_topology · Uses: G001, S016





S018 · impliesBefore

ORIGINAL target-open index=0,O=[];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S017





S019 · impliesBefore

ORIGINAL target-open index=1,O=[0];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[0];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S018





S020 · impliesBefore

ORIGINAL target-open index=2,O=[0, 1];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[0];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S019





S021 · impliesBefore

ORIGINAL target-open index=3,O=[0, 1, 2];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[0, 1, 2];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S020





S022 · impliesBefore

ORIGINAL target-open index=4,O=[0, 2];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[0, 1, 2];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S021





S023 · impliesBefore

ORIGINAL target-open index=5,O=[1];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S022





S024 · impliesBefore

ORIGINAL target-open index=6,O=[1, 2];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[1, 2];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S023





S025 · impliesBefore

ORIGINAL target-open index=7,O=[2];total original map=[0, 2, 2];ENTIRE source carrier Fin(3)

After

full source preimage=[1, 2];source-open=Yes;NOT restricted to K

Conditions: none

Continuity checks every target-open preimage in the entire source,not just K or sampled opens.A failed source-open test remains false.

Step identifiers and dependenciesRule: compactimg_EVERY_target_open_FULL_source_preimage · Uses: G001, S024





S026 · impliesBefore

ORIGINAL source subset K=[0, 1, 2];ALL [x,map(x)] pairs=[[0, 0], [1, 2], [2, 2]];target carrier Fin(3)

After

exact sorted distinct image=[0, 2];K and image finite hence compact;continuous=Yes is the ALL-target-open conjunction

Conditions: none

Every image value has an original K witness and every K image is included,so the set is exactly f(K).A finite set has a finite subcover by choosing one cover member per point.This finite argument is separate from continuity and from the general pullback theorem.

Step identifiers and dependenciesRule: compactimg_finite_image_and_continuity_separate · Uses: G001, S025









## Reverse checks


- S026 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S025 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S024 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S023 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S022 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S021 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S020 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S019 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S018 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S017 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S016 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S015 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S014 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S012 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.





## Result

([[[], []], [[0], [0]], [[0, 1], [0]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [1, 2]], [[2], [1, 2]]], Yes, every_target_open_has_source_open_preimage)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: d681f1e804e5d961c1c1d88bb10504252d378a4060c38c654458f89ad29eee8a
- candidate record SHA-256: c02de5a21271c8822aa17419631c01a4866112ef60633d5bcd78f1140300956d
- semantic review receipt SHA-256: 49cf6ec60211c92d1c0c302663af4d44479635dc8181fb61a20c3374288e21c5
- question-first witness SHA-256: 10fd25b4643e5ff12753daceaa61f9f2499bf381f65ef96e9d21185c7c0d0c5e
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0050.json)