{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Q4VWJWKOYTKZM6NLJ7VXI3VOID","short_pith_number":"pith:Q4VWJWKO","canonical_record":{"source":{"id":"2605.14076","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T19:55:00Z","cross_cats_sorted":[],"title_canon_sha256":"0fcd5d1f0397675ea15b63c2889b612f4ddbeb9f39dd53ca231aaab28455f5b3","abstract_canon_sha256":"e5e5fda998c68d7c7b1af1b503f218b5100ac8a92839827fad28fc04c3f4362c"},"schema_version":"1.0"},"canonical_sha256":"872b64d94ec4d59679ab4feb746eae40c0dc283ab7cde9ea08de03cdf7ba1f22","source":{"kind":"arxiv","id":"2605.14076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14076","created_at":"2026-05-17T23:39:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14076v1","created_at":"2026-05-17T23:39:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14076","created_at":"2026-05-17T23:39:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q4VWJWKOYTKZ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4VWJWKOYTKZM6NL","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4VWJWKO","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Q4VWJWKOYTKZM6NLJ7VXI3VOID","target":"record","payload":{"canonical_record":{"source":{"id":"2605.14076","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T19:55:00Z","cross_cats_sorted":[],"title_canon_sha256":"0fcd5d1f0397675ea15b63c2889b612f4ddbeb9f39dd53ca231aaab28455f5b3","abstract_canon_sha256":"e5e5fda998c68d7c7b1af1b503f218b5100ac8a92839827fad28fc04c3f4362c"},"schema_version":"1.0"},"canonical_sha256":"872b64d94ec4d59679ab4feb746eae40c0dc283ab7cde9ea08de03cdf7ba1f22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:12.363451Z","signature_b64":"MdekKzWNL9rmfHuZEd/QZ3TGwO2jzmZQ2OME5MYZjF7M156wRKlx8NJMDF3h7mvShzWOWU3NOx0Y0rCyeakuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"872b64d94ec4d59679ab4feb746eae40c0dc283ab7cde9ea08de03cdf7ba1f22","last_reissued_at":"2026-05-17T23:39:12.362638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:12.362638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.14076","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbLIr56DTLP8U5VLIlrCPkjSmd7kmiMN9yheDCgPPBzTSW4DTlQ8QfC0AuXuHkFJECBQELhDFiet/9Rs6qysDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:50:47.291927Z"},"content_sha256":"742c21d1171ede2fa168d4df823db5cd0ec9ff0ea57aa8510f59965572288b7b","schema_version":"1.0","event_id":"sha256:742c21d1171ede2fa168d4df823db5cd0ec9ff0ea57aa8510f59965572288b7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Q4VWJWKOYTKZM6NLJ7VXI3VOID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 2-Quasi-Regularizability Conjecture and Independence Polynomials of Wp Graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"A connected W_2 graph is 2-quasi-regularizable exactly when n(G) is at least 3α(G).","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kevin Pereyra","submitted_at":"2026-05-13T19:55:00Z","abstract_excerpt":"Hoang, Levit, Mandrescu and Pham asked for structural conditions ensuring that the independence polynomial of a $\\W_p$ graph is log-concave, or at least unimodal, and conjectured that a connected $\\W_2$ graph is $2$-quasi-regularizable if and only if $n(G)\\ge 3\\alpha(G)$ (2026). We prove the conjecture. The key point is a local expansion theorem: if $G$ is connected and belongs to $\\W_2$, then every non-maximum independent set $A$ satisfies \\[ |N_G(A)|\\ge 2|A|. \\] Thus the only possible obstruction to $2$-quasi-regularizability in a connected $\\W_2$ graph comes from maximum independent sets, w"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove the conjecture. The key point is a local expansion theorem: if G is connected and belongs to W_2, then every non-maximum independent set A satisfies |N_G(A)| ≥ 2|A|. Thus the only possible obstruction to 2-quasi-regularizability in a connected W_2 graph comes from maximum independent sets, where the condition is exactly n(G)−α(G)≥2α(G).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that G is connected and lies in the class W_2; the local expansion theorem is stated only under these hypotheses, so the reduction to the numerical condition on maximum independent sets holds only inside this restricted family.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves the 2-quasi-regularizability conjecture for connected W_2 graphs via a local expansion theorem and derives explicit log-concavity and unimodality regions for their independence polynomials.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A connected W_2 graph is 2-quasi-regularizable exactly when n(G) is at least 3α(G).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fded09d216420119537d7fabc7977a262b859a20498b6ba2ec3eb19f612de38d"},"source":{"id":"2605.14076","kind":"arxiv","version":1},"verdict":{"id":"f5618d56-e673-460c-805d-cdb4a98f8e19","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:33:53.185431Z","strongest_claim":"We prove the conjecture. The key point is a local expansion theorem: if G is connected and belongs to W_2, then every non-maximum independent set A satisfies |N_G(A)| ≥ 2|A|. Thus the only possible obstruction to 2-quasi-regularizability in a connected W_2 graph comes from maximum independent sets, where the condition is exactly n(G)−α(G)≥2α(G).","one_line_summary":"Proves the 2-quasi-regularizability conjecture for connected W_2 graphs via a local expansion theorem and derives explicit log-concavity and unimodality regions for their independence polynomials.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that G is connected and lies in the class W_2; the local expansion theorem is stated only under these hypotheses, so the reduction to the numerical condition on maximum independent sets holds only inside this restricted family.","pith_extraction_headline":"A connected W_2 graph is 2-quasi-regularizable exactly when n(G) is at least 3α(G)."},"references":{"count":37,"sample":[{"doi":"","year":1987,"title":"Y. Alavi, P. J. Malde, A. J. Schwenk, and P. Erdos,The vertex independence sequence of a graph is not constrained, Congressus Numerantium58(1987), 15–23","work_id":"a3149759-9ff0-42cf-b3dd-2ec84944bdfa","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1982,"title":"Berge,Some common properties for regularizable graphs, edge-critical graphs and B-graphs, Annals of Discrete Mathematics12(1982), 31–44","work_id":"1ff9ae94-c6d7-4cba-a179-c99bb16d63f7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"J. I. Brown, C. A. Hickman, and R. J. Nowakowski,On the location of roots of independence polynomials, Journal of Algebraic Combinatorics19(2004), 273–282","work_id":"c697f66b-865f-4554-88d6-724f68067d3b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"S.-Y. Chen and H.-J. Wang,Unimodality of very well-covered graphs, Ars Combina- toria97A(2010), 509–529","work_id":"e0599989-2042-428e-9c33-f0689480f2db","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"M. Chudnovsky and P. Seymour,The roots of the independence polynomial of a claw-free graph, Journal of Combinatorial Theory, Series B97(2007), 350–357","work_id":"2732c7ce-7806-4c45-b785-124da29f9fa3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"1ff6c16161bfdbd85956682e065f27cafa54a92b5897af3fae23862ea64dbd3e","internal_anchors":2},"formal_canon":{"evidence_count":1,"snapshot_sha256":"e407366cb07fa2b72078e62cfb3f762b69ed126331c3f6d4e5b9f6af2be7b05b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"f5618d56-e673-460c-805d-cdb4a98f8e19"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqSRDzd9b2K0xR99Mr+EDs211qoxnLUgTMoImkiQHXh02SV46FUpQvQ6Az+/LPp1z3ssJ0sirnyZJ0RIhrItDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:50:47.292612Z"},"content_sha256":"6639b8b313709bd2ac71c0d4a6a18c22db38d9c0c38d60fd9ca67052f830e9c4","schema_version":"1.0","event_id":"sha256:6639b8b313709bd2ac71c0d4a6a18c22db38d9c0c38d60fd9ca67052f830e9c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID/bundle.json","state_url":"https://pith.science/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T10:50:47Z","links":{"resolver":"https://pith.science/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID","bundle":"https://pith.science/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID/bundle.json","state":"https://pith.science/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4VWJWKOYTKZM6NLJ7VXI3VOID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Q4VWJWKOYTKZM6NLJ7VXI3VOID","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e5e5fda998c68d7c7b1af1b503f218b5100ac8a92839827fad28fc04c3f4362c","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T19:55:00Z","title_canon_sha256":"0fcd5d1f0397675ea15b63c2889b612f4ddbeb9f39dd53ca231aaab28455f5b3"},"schema_version":"1.0","source":{"id":"2605.14076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14076","created_at":"2026-05-17T23:39:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14076v1","created_at":"2026-05-17T23:39:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14076","created_at":"2026-05-17T23:39:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q4VWJWKOYTKZ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4VWJWKOYTKZM6NL","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4VWJWKO","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:6639b8b313709bd2ac71c0d4a6a18c22db38d9c0c38d60fd9ca67052f830e9c4","target":"graph","created_at":"2026-05-17T23:39:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove the conjecture. The key point is a local expansion theorem: if G is connected and belongs to W_2, then every non-maximum independent set A satisfies |N_G(A)| ≥ 2|A|. Thus the only possible obstruction to 2-quasi-regularizability in a connected W_2 graph comes from maximum independent sets, where the condition is exactly n(G)−α(G)≥2α(G)."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that G is connected and lies in the class W_2; the local expansion theorem is stated only under these hypotheses, so the reduction to the numerical condition on maximum independent sets holds only inside this restricted family."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves the 2-quasi-regularizability conjecture for connected W_2 graphs via a local expansion theorem and derives explicit log-concavity and unimodality regions for their independence polynomials."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A connected W_2 graph is 2-quasi-regularizable exactly when n(G) is at least 3α(G)."}],"snapshot_sha256":"fded09d216420119537d7fabc7977a262b859a20498b6ba2ec3eb19f612de38d"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"e407366cb07fa2b72078e62cfb3f762b69ed126331c3f6d4e5b9f6af2be7b05b"},"paper":{"abstract_excerpt":"Hoang, Levit, Mandrescu and Pham asked for structural conditions ensuring that the independence polynomial of a $\\W_p$ graph is log-concave, or at least unimodal, and conjectured that a connected $\\W_2$ graph is $2$-quasi-regularizable if and only if $n(G)\\ge 3\\alpha(G)$ (2026). We prove the conjecture. The key point is a local expansion theorem: if $G$ is connected and belongs to $\\W_2$, then every non-maximum independent set $A$ satisfies \\[ |N_G(A)|\\ge 2|A|. \\] Thus the only possible obstruction to $2$-quasi-regularizability in a connected $\\W_2$ graph comes from maximum independent sets, w","authors_text":"Kevin Pereyra","cross_cats":[],"headline":"A connected W_2 graph is 2-quasi-regularizable exactly when n(G) is at least 3α(G).","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T19:55:00Z","title":"The 2-Quasi-Regularizability Conjecture and Independence Polynomials of Wp Graphs"},"references":{"count":37,"internal_anchors":2,"resolved_work":37,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Y. Alavi, P. J. Malde, A. J. Schwenk, and P. Erdos,The vertex independence sequence of a graph is not constrained, Congressus Numerantium58(1987), 15–23","work_id":"a3149759-9ff0-42cf-b3dd-2ec84944bdfa","year":1987},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Berge,Some common properties for regularizable graphs, edge-critical graphs and B-graphs, Annals of Discrete Mathematics12(1982), 31–44","work_id":"1ff9ae94-c6d7-4cba-a179-c99bb16d63f7","year":1982},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"J. I. Brown, C. A. Hickman, and R. J. Nowakowski,On the location of roots of independence polynomials, Journal of Algebraic Combinatorics19(2004), 273–282","work_id":"c697f66b-865f-4554-88d6-724f68067d3b","year":2004},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"S.-Y. Chen and H.-J. Wang,Unimodality of very well-covered graphs, Ars Combina- toria97A(2010), 509–529","work_id":"e0599989-2042-428e-9c33-f0689480f2db","year":2010},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"M. Chudnovsky and P. Seymour,The roots of the independence polynomial of a claw-free graph, Journal of Combinatorial Theory, Series B97(2007), 350–357","work_id":"2732c7ce-7806-4c45-b785-124da29f9fa3","year":2007}],"snapshot_sha256":"1ff6c16161bfdbd85956682e065f27cafa54a92b5897af3fae23862ea64dbd3e"},"source":{"id":"2605.14076","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T02:33:53.185431Z","id":"f5618d56-e673-460c-805d-cdb4a98f8e19","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves the 2-quasi-regularizability conjecture for connected W_2 graphs via a local expansion theorem and derives explicit log-concavity and unimodality regions for their independence polynomials.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A connected W_2 graph is 2-quasi-regularizable exactly when n(G) is at least 3α(G).","strongest_claim":"We prove the conjecture. The key point is a local expansion theorem: if G is connected and belongs to W_2, then every non-maximum independent set A satisfies |N_G(A)| ≥ 2|A|. Thus the only possible obstruction to 2-quasi-regularizability in a connected W_2 graph comes from maximum independent sets, where the condition is exactly n(G)−α(G)≥2α(G).","weakest_assumption":"The assumption that G is connected and lies in the class W_2; the local expansion theorem is stated only under these hypotheses, so the reduction to the numerical condition on maximum independent sets holds only inside this restricted family."}},"verdict_id":"f5618d56-e673-460c-805d-cdb4a98f8e19"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:742c21d1171ede2fa168d4df823db5cd0ec9ff0ea57aa8510f59965572288b7b","target":"record","created_at":"2026-05-17T23:39:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e5e5fda998c68d7c7b1af1b503f218b5100ac8a92839827fad28fc04c3f4362c","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T19:55:00Z","title_canon_sha256":"0fcd5d1f0397675ea15b63c2889b612f4ddbeb9f39dd53ca231aaab28455f5b3"},"schema_version":"1.0","source":{"id":"2605.14076","kind":"arxiv","version":1}},"canonical_sha256":"872b64d94ec4d59679ab4feb746eae40c0dc283ab7cde9ea08de03cdf7ba1f22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"872b64d94ec4d59679ab4feb746eae40c0dc283ab7cde9ea08de03cdf7ba1f22","first_computed_at":"2026-05-17T23:39:12.362638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:12.362638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MdekKzWNL9rmfHuZEd/QZ3TGwO2jzmZQ2OME5MYZjF7M156wRKlx8NJMDF3h7mvShzWOWU3NOx0Y0rCyeakuBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:12.363451Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:742c21d1171ede2fa168d4df823db5cd0ec9ff0ea57aa8510f59965572288b7b","sha256:6639b8b313709bd2ac71c0d4a6a18c22db38d9c0c38d60fd9ca67052f830e9c4"],"state_sha256":"9d10cc10485d00d29f1d77016fbb36bb82f6a702e6ef444c3199127efa443b85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k5cuZBDW2hhkjFffZuTZ0ZGWifEK1L164M7sXtbglAdvXrRu+5HYhPgv5AQ+zXUBsRuAVLZduZfBbbq6/UW0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:50:47.295248Z","bundle_sha256":"bfb7f5373e38b89c77b7c944f37adec60456b8431d63e3934286986badfc9824"}}