{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4TPM7YRSSADUBTFWLWFKSVSQCY","short_pith_number":"pith:4TPM7YRS","canonical_record":{"source":{"id":"2407.17826","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-25T07:31:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"81d874fb0b9eb47382cbb27933deaed3d1065ae19a8fc58512a387117ceffd51","abstract_canon_sha256":"4e053f0cafad9cbd8568e3c0cd1ce73fb4bda04cefdbcc172ff9308ffb626284"},"schema_version":"1.0"},"canonical_sha256":"e4decfe232900740ccb65d8aa95650163de7897a6c1400a9b2d0c135ab808412","source":{"kind":"arxiv","id":"2407.17826","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17826","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17826v4","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17826","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"4TPM7YRSSADU","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"pith_short_16","alias_value":"4TPM7YRSSADUBTFW","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"pith_short_8","alias_value":"4TPM7YRS","created_at":"2026-07-05T10:07:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4TPM7YRSSADUBTFWLWFKSVSQCY","target":"record","payload":{"canonical_record":{"source":{"id":"2407.17826","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-25T07:31:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"81d874fb0b9eb47382cbb27933deaed3d1065ae19a8fc58512a387117ceffd51","abstract_canon_sha256":"4e053f0cafad9cbd8568e3c0cd1ce73fb4bda04cefdbcc172ff9308ffb626284"},"schema_version":"1.0"},"canonical_sha256":"e4decfe232900740ccb65d8aa95650163de7897a6c1400a9b2d0c135ab808412","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:25.886632Z","signature_b64":"vUUP/4hmYOAJjm9fw/tRcNRO/CJUKNF6A8K5LpwCJX7Q7pURcI0CffBl4IRc/4vFHEH2itQKCP76VYal/WEXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4decfe232900740ccb65d8aa95650163de7897a6c1400a9b2d0c135ab808412","last_reissued_at":"2026-07-05T10:07:25.886111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:25.886111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.17826","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qULXPH3WUEZToTQLIj5fNWi86RZ+L1NAuvk50UyH85fTOiRNYLRGB+gYsGLL6+Eh4rj6b3wBsCLwNCbFuHpPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:24:49.263965Z"},"content_sha256":"b42dadfc065b814473728d7b87591be20f406b15e77bd84da759b8bba8e7cb9e","schema_version":"1.0","event_id":"sha256:b42dadfc065b814473728d7b87591be20f406b15e77bd84da759b8bba8e7cb9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4TPM7YRSSADUBTFWLWFKSVSQCY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sign patterns of principal minors of real symmetric matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Jesse Selover, Maksym Zubkov, Tobias Boege","submitted_at":"2024-07-25T07:31:35Z","abstract_excerpt":"We analyze a combinatorial rule satisfied by the signs of principal minors of a real symmetric matrix. The sign patterns satisfying this rule are equivalent to uniform oriented Lagrangian matroids. We first discuss their structure and symmetries and then study their asymptotics, proving that almost all of them are not representable by real symmetric matrices. We offer several conjectures and experimental results concerning representable sign patterns and the topology of their representation spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17826","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.17826/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCx0xVVJP9zMD4MQ7dWymvHct43Si7IKZpenlgRbazEp4EPqcdhIJCoDKEQeHML6wT/2GpIOtbm4SY4OMCfcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:24:49.264337Z"},"content_sha256":"54294f6a89281599448f0a38d6cbddafcc9778380a2bcc1328281091f4a3c84a","schema_version":"1.0","event_id":"sha256:54294f6a89281599448f0a38d6cbddafcc9778380a2bcc1328281091f4a3c84a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TPM7YRSSADUBTFWLWFKSVSQCY/bundle.json","state_url":"https://pith.science/pith/4TPM7YRSSADUBTFWLWFKSVSQCY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TPM7YRSSADUBTFWLWFKSVSQCY/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":"2026-07-06T16:24:49Z","links":{"resolver":"https://pith.science/pith/4TPM7YRSSADUBTFWLWFKSVSQCY","bundle":"https://pith.science/pith/4TPM7YRSSADUBTFWLWFKSVSQCY/bundle.json","state":"https://pith.science/pith/4TPM7YRSSADUBTFWLWFKSVSQCY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TPM7YRSSADUBTFWLWFKSVSQCY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4TPM7YRSSADUBTFWLWFKSVSQCY","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":"4e053f0cafad9cbd8568e3c0cd1ce73fb4bda04cefdbcc172ff9308ffb626284","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-25T07:31:35Z","title_canon_sha256":"81d874fb0b9eb47382cbb27933deaed3d1065ae19a8fc58512a387117ceffd51"},"schema_version":"1.0","source":{"id":"2407.17826","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17826","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17826v4","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17826","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"4TPM7YRSSADU","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"pith_short_16","alias_value":"4TPM7YRSSADUBTFW","created_at":"2026-07-05T10:07:25Z"},{"alias_kind":"pith_short_8","alias_value":"4TPM7YRS","created_at":"2026-07-05T10:07:25Z"}],"graph_snapshots":[{"event_id":"sha256:54294f6a89281599448f0a38d6cbddafcc9778380a2bcc1328281091f4a3c84a","target":"graph","created_at":"2026-07-05T10:07:25Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.17826/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze a combinatorial rule satisfied by the signs of principal minors of a real symmetric matrix. The sign patterns satisfying this rule are equivalent to uniform oriented Lagrangian matroids. We first discuss their structure and symmetries and then study their asymptotics, proving that almost all of them are not representable by real symmetric matrices. We offer several conjectures and experimental results concerning representable sign patterns and the topology of their representation spaces.","authors_text":"Jesse Selover, Maksym Zubkov, Tobias Boege","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-25T07:31:35Z","title":"Sign patterns of principal minors of real symmetric matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17826","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b42dadfc065b814473728d7b87591be20f406b15e77bd84da759b8bba8e7cb9e","target":"record","created_at":"2026-07-05T10:07:25Z","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":"4e053f0cafad9cbd8568e3c0cd1ce73fb4bda04cefdbcc172ff9308ffb626284","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-25T07:31:35Z","title_canon_sha256":"81d874fb0b9eb47382cbb27933deaed3d1065ae19a8fc58512a387117ceffd51"},"schema_version":"1.0","source":{"id":"2407.17826","kind":"arxiv","version":4}},"canonical_sha256":"e4decfe232900740ccb65d8aa95650163de7897a6c1400a9b2d0c135ab808412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4decfe232900740ccb65d8aa95650163de7897a6c1400a9b2d0c135ab808412","first_computed_at":"2026-07-05T10:07:25.886111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:25.886111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vUUP/4hmYOAJjm9fw/tRcNRO/CJUKNF6A8K5LpwCJX7Q7pURcI0CffBl4IRc/4vFHEH2itQKCP76VYal/WEXCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:25.886632Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.17826","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b42dadfc065b814473728d7b87591be20f406b15e77bd84da759b8bba8e7cb9e","sha256:54294f6a89281599448f0a38d6cbddafcc9778380a2bcc1328281091f4a3c84a"],"state_sha256":"8b9f3679e92a1054635d35ca9d65dbb94366acebc29ff43673fc946729493d82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDwKYxop1S172mlsXSHgNAkSb/bn+u8pYRWg2VKPQ9P+E/NakJbyRz2GrR0A2P4WPpflSTdonUrts0usA5Z9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T16:24:49.266181Z","bundle_sha256":"5a623393064896602c47da9eab62d66ad250fd5732ea016425cafc63ffae4723"}}