{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:J6RU4XHQMKEBPUNTZ55HBCGXCU","short_pith_number":"pith:J6RU4XHQ","canonical_record":{"source":{"id":"1612.08651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-27T14:58:17Z","cross_cats_sorted":[],"title_canon_sha256":"e2b1a720401adecb21f2c5aeb3c69e1e9bfa2082c31d96074222bb1ca78fa3c9","abstract_canon_sha256":"5b977d9322d06388a0dfc02f6316e24a7d834bf9dda0dbf14f3ba46b8c601d6d"},"schema_version":"1.0"},"canonical_sha256":"4fa34e5cf0628817d1b3cf7a7088d7150be501018285b7fe73f5b758540e7e7e","source":{"kind":"arxiv","id":"1612.08651","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08651","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08651v2","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08651","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"J6RU4XHQMKEB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J6RU4XHQMKEBPUNT","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J6RU4XHQ","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:J6RU4XHQMKEBPUNTZ55HBCGXCU","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-27T14:58:17Z","cross_cats_sorted":[],"title_canon_sha256":"e2b1a720401adecb21f2c5aeb3c69e1e9bfa2082c31d96074222bb1ca78fa3c9","abstract_canon_sha256":"5b977d9322d06388a0dfc02f6316e24a7d834bf9dda0dbf14f3ba46b8c601d6d"},"schema_version":"1.0"},"canonical_sha256":"4fa34e5cf0628817d1b3cf7a7088d7150be501018285b7fe73f5b758540e7e7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:21.883451Z","signature_b64":"fZE39RF5kG43WTMVNhULUZYBJxKiC7YsZzPPNRqkmC/RDD8RB47rYSnvz70YBJVHV9aKAP6OCbdTtqoF/Ee/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fa34e5cf0628817d1b3cf7a7088d7150be501018285b7fe73f5b758540e7e7e","last_reissued_at":"2026-05-18T00:27:21.882851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:21.882851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08651","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoNT+XGTlIr9JTbViuRc9s6hqHbDt2NURAkOY4m5u2wUJFSotIRLCnEV7xQUIJakJR/8jlgIgcVjizorh8XCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:18:42.960780Z"},"content_sha256":"795d7cf0af5aab014fec6c60ec67f4745433e017afaa8bbf33f19fd4d69d976d","schema_version":"1.0","event_id":"sha256:795d7cf0af5aab014fec6c60ec67f4745433e017afaa8bbf33f19fd4d69d976d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:J6RU4XHQMKEBPUNTZ55HBCGXCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secant degeneracy index of the standard strata in the space of binary forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris Shapiro, Gleb Nenashev, Michael Shapiro","submitted_at":"2016-12-27T14:58:17Z","abstract_excerpt":"The space $Pol_d\\simeq \\bC P^d$ of all complex-valued binary forms of degree $d$ (considered up to a constant factor) has a standard stratification, each stratum of which contains all forms whose set of multiplicities of their distinct roots is given by a fixed partition $\\mu \\vdash d$. For each such stratum $S_\\mu,$ we introduce its secant degeneracy index $\\ell_\\mu$ which is the minimal number of projectively dependent pairwise distinct points on $S_\\mu$, i.e., points whose projective span has dimension smaller than $\\ell_\\mu-1$. In what follows, we discuss the secant degeneracy index $\\ell_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08651","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoKis1q7m94hSR6g1dc9LzfagvcUI3l7JeZkiBOqvG//RHjesLC/chl4r8mh3uPs4J+WPm5upwP7h0BUutKlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:18:42.961130Z"},"content_sha256":"084a185fed2445d503c4b4fb65ee1d22dee673a109b1436df5b76470e205e923","schema_version":"1.0","event_id":"sha256:084a185fed2445d503c4b4fb65ee1d22dee673a109b1436df5b76470e205e923"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU/bundle.json","state_url":"https://pith.science/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU/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":"2026-05-27T07:18:42Z","links":{"resolver":"https://pith.science/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU","bundle":"https://pith.science/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU/bundle.json","state":"https://pith.science/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6RU4XHQMKEBPUNTZ55HBCGXCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J6RU4XHQMKEBPUNTZ55HBCGXCU","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":"5b977d9322d06388a0dfc02f6316e24a7d834bf9dda0dbf14f3ba46b8c601d6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-27T14:58:17Z","title_canon_sha256":"e2b1a720401adecb21f2c5aeb3c69e1e9bfa2082c31d96074222bb1ca78fa3c9"},"schema_version":"1.0","source":{"id":"1612.08651","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08651","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08651v2","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08651","created_at":"2026-05-18T00:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"J6RU4XHQMKEB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J6RU4XHQMKEBPUNT","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J6RU4XHQ","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:084a185fed2445d503c4b4fb65ee1d22dee673a109b1436df5b76470e205e923","target":"graph","created_at":"2026-05-18T00:27:21Z","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"},"paper":{"abstract_excerpt":"The space $Pol_d\\simeq \\bC P^d$ of all complex-valued binary forms of degree $d$ (considered up to a constant factor) has a standard stratification, each stratum of which contains all forms whose set of multiplicities of their distinct roots is given by a fixed partition $\\mu \\vdash d$. For each such stratum $S_\\mu,$ we introduce its secant degeneracy index $\\ell_\\mu$ which is the minimal number of projectively dependent pairwise distinct points on $S_\\mu$, i.e., points whose projective span has dimension smaller than $\\ell_\\mu-1$. In what follows, we discuss the secant degeneracy index $\\ell_","authors_text":"Boris Shapiro, Gleb Nenashev, Michael Shapiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-27T14:58:17Z","title":"Secant degeneracy index of the standard strata in the space of binary forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08651","kind":"arxiv","version":2},"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":"sha256:795d7cf0af5aab014fec6c60ec67f4745433e017afaa8bbf33f19fd4d69d976d","target":"record","created_at":"2026-05-18T00:27:21Z","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":"5b977d9322d06388a0dfc02f6316e24a7d834bf9dda0dbf14f3ba46b8c601d6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-27T14:58:17Z","title_canon_sha256":"e2b1a720401adecb21f2c5aeb3c69e1e9bfa2082c31d96074222bb1ca78fa3c9"},"schema_version":"1.0","source":{"id":"1612.08651","kind":"arxiv","version":2}},"canonical_sha256":"4fa34e5cf0628817d1b3cf7a7088d7150be501018285b7fe73f5b758540e7e7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fa34e5cf0628817d1b3cf7a7088d7150be501018285b7fe73f5b758540e7e7e","first_computed_at":"2026-05-18T00:27:21.882851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:21.882851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fZE39RF5kG43WTMVNhULUZYBJxKiC7YsZzPPNRqkmC/RDD8RB47rYSnvz70YBJVHV9aKAP6OCbdTtqoF/Ee/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:21.883451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08651","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:795d7cf0af5aab014fec6c60ec67f4745433e017afaa8bbf33f19fd4d69d976d","sha256:084a185fed2445d503c4b4fb65ee1d22dee673a109b1436df5b76470e205e923"],"state_sha256":"59abf46b58f4a4d53cd1fe1c6c65833fa6ab31d5e4726f450cea7553cb40da73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQg7JEgIU2vuP5w2DfaVMqOpO3j6pIe0mDZsxJ4LD+x/v5bWGhCMtSp/1eN8DtKeMgRAUaVCI7vOqU2dDWR5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:18:42.963133Z","bundle_sha256":"f9e11810389bd502aac8752d3ed3b675004dac786d1b04e2add2ef13ae24ac97"}}